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# Selina solutions Selina ICSE Concise Mathematics for Class 10 chapter 13 Section and Mid-Point Formula

## Chapter 13 - Section and Mid-Point Formula

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Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

Find, if (1,3) lie on the line x – 2y + 5 = 0

Calculate the co-ordinates of the point P which divides the line segment joining: A (1, 3) and B (5, 9) in the ratio 1 : 2

Calculate the co-ordinates of the point P which divides the line segment joining: A (1, 3) and B (5, 9) in the ratio 1 : 2

Find, if point (0,5) lie on the line x – 2y + 5 = 0

Calculate the co-ordinates of the point P which divides the line segment joining:  A (-4, 6) and B(3, -5) in the ratio 3 : 2

Calculate the co-ordinates of the point P which divides the line segment joining:  A (-4, 6) and B(3, -5) in the ratio 3 : 2

Find, if point (-5,0) lie on the line x – 2y + 5 = 0

Find, if point (5,5) lie on the line x – 2y + 5 = 0

State, true or false: the point (-3, 0) lies on the line x + 3 = 0

Find, if point (2,-1.5) lie on the line x – 2y + 5 = 0

State, true or false: if the point (2, a) lies on the line 2x – y = 3, then a = 5.

Find, if point (-2,-1.5) lie on the line x – 2y + 5 = 0

In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis.

In what ratio is the line joining (2, -3) and (5, 6) divided by the x-axis.

State, true or false : the line x/ y+y/3=0 passes through the point (2, 3)

State, true or false: the line x/2+y/3=0 passes through the point (4, -6)

State, true or false: the point (8, 7) lies on the line y – 7 = 0

The line given by the equation 2x-y/3=7 passes through the point (k, 6); calculate the value of k.

In what ratio is the line joining (2, -4) and (-3, 6) divided by the y – axis.

In what ratio is the line joining (2, -4) and (-3, 6) divided by the y – axis.

For what value of k will the point (3, −k) lie on the line 9x + 4y = 3?

In what ratio does the point (1, a) divide the join of (-1, 4) and (4,-1)? Also, find the value of a.

In what ratio does the point (1, a) divide the join of (-1, 4) and (4,-1)? Also, find the value of a.

The line (3x)/5-(2y)/3+1=0 contains the point (m, 2m – 1); calculate the value of m.

In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8)? Also, find the value of a.

In what ratio does the point (a, 6) divide the join of (-4, 3) and (2, 8)? Also, find the value of a.

In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-ordinates of the point of intersection.

In what ratio is the join of (4, 3) and (2, -6) divided by the x-axis. Also, find the co-ordinates of the point of intersection.

Does the line 3x − 5y = 6 bisect the join of (5, −2) and (−1, 2)?

Find the ratio in which the join of (-4, 7) and (3, 0) is divided by the y-axis. Also, find the coordinates of the point of intersection.

Find the ratio in which the join of (-4, 7) and (3, 0) is divided by the y-axis. Also, find the coordinates of the point of intersection.

the line y = 3x – 2 bisects the join of (a, 3) and (2, −5), Find the value of a.

the line x – 6y + 11 = 0 bisects the join of (8, −1) and (0, k). Find the value of k.

Points A, B, C and D divide the line segment joining the point (5, -10) and the origin in five equal parts. Find the co-ordinates of B and D.

Points A, B, C and D divide the line segment joining the point (5, -10) and the origin in five equal parts. Find the co-ordinates of B and D.

the point (−3, 2) lies on the line ax + 3y + 6 = 0, calculate the value of a.

The line y = mx + 8 contains the point (−4, 4), calculate the value of m.

The line joining the points A (-3, -10) and B (-2, 6) is divided by the point P such that (PB)/(AB)=1/5 Find the co-ordinates of P.

The point P divides the join of (2, 1) and (−3, 6) in the ratio 2 : 3. Does P lies on the line x − 5y + 15 = 0?

The line joining the points A (-3, -10) and B (-2, 6) is divided by the point P such that (PB)/(AB)=1/5 Find the co-ordinates of P.

The line segment joining the points (5, −4) and (2, 2) is divided by the points Q in the ratio 1:2 Does the line x – 2y = 0 contain Q?

P is a point on the line joining A(4, 3) and B(-2, 6) such that 5AP = 2BP. Find the co-ordinates of P.

P is a point on the line joining A(4, 3) and B(-2, 6) such that 5AP = 2BP. Find the co-ordinates of P.

Find the point of intersection of the lines: 4x + 3y = 1 and 3x − y + 9 = 0. If this point lies on the line (2k – 1) x – 2y = 4; find the value of k.

Calculate the ratio in which the line joining the points (-3, -1) and (5, 7) is divided by the line x = 2. Also, find the co-ordinates of the point of intersection.

Calculate the ratio in which the line joining the points (-3, -1) and (5, 7) is divided by the line x = 2. Also, find the co-ordinates of the point of intersection.

Show that the lines 2x + 5y = 1, x – 3y = 6 and x + 5y + 2 = 0 are concurrent.

Calculate the ratio in which the line joining A(6, 5) and B(4, -3) is divided by the line y = 2.

Calculate the ratio in which the line joining A(6, 5) and B(4, -3) is divided by the line y = 2.

The point P (5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B.

Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

Show that the line segment joining the points (-5, 8) and (10, -4) is trisected by the co-ordinate axes.

The point P (5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the co-ordinates of points A and B.

Find the co-ordinates of the points of tri-section of the line joining the points (-3, 0) and (6, 6)

Find the co-ordinates of the points of tri-section of the line joining the points (-3, 0) and (6, 6)

Show that A (3, -2) is a point of trisection of the line segment joining the points (2, 1) and (5, -8).
Also, find the co-ordinates of the other point of trisection.

Show that A (3, -2) is a point of trisection of the line segment joining the points (2, 1) and (5, -8).
Also, find the co-ordinates of the other point of trisection.

If A = (-4, 3) and B = (8, -6)
(i) Find the length of AB
(ii) In what ratio is the line joining A and B, divided by the x-axis?

If A = (-4, 3) and B = (8, -6)
(i) Find the length of AB
(ii) In what ratio is the line joining A and B, divided by the x-axis?

The line segment joining the points M(5, 7) and N(-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

The line segment joining the points M(5, 7) and N(-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

A (2, 5), B (-1, 2) and C (5, 8) are the co-ordinates of the vertices of the triangle ABC. Points P
and Q lie on AB and AC respectively,
Such that: AP : PB = AQ : QC = 1 : 2
(i) Calculate the co-ordinates of P and Q.
(ii) Show that PQ =1/3BC

A (2, 5), B (-1, 2) and C (5, 8) are the co-ordinates of the vertices of the triangle ABC. Points P
and Q lie on AB and AC respectively,
Such that: AP : PB = AQ : QC = 1 : 2
(i) Calculate the co-ordinates of P and Q.
(ii) Show that PQ =1/3BC

A (-3, 4), B (3, -1) and C (-2, 4) are the vertices of a triangle ABC. Find the length of line segment AP, where point P lies inside BC, such that BP : PC = 2 : 3

A (-3, 4), B (3, -1) and C (-2, 4) are the vertices of a triangle ABC. Find the length of line segment AP, where point P lies inside BC, such that BP : PC = 2 : 3

The line segment joining A (2, 3) and B (6, -5) is intercepted by x-axis at the point K. Write down the ordinate of the point K. Hence, find the ratio in which K divides AB. Also find the coordinates of the point K.

The line segment joining A (2, 3) and B (6, -5) is intercepted by x-axis at the point K. Write down the ordinate of the point K. Hence, find the ratio in which K divides AB. Also find the coordinates of the point K.

The line segment joining A (4, 7) and B (-6, -2) is intercepted by the y – axis at the point K. write down the abscissa of the point K. hence, find the ratio in which K divides AB. Also, find the co-ordinates of the point K.

The line segment joining A (4, 7) and B (-6, -2) is intercepted by the y – axis at the point K. write down the abscissa of the point K. hence, find the ratio in which K divides AB. Also, find the co-ordinates of the point K.

The line joining P(-4, 5) and Q(3, 2) intersects the y-axis at point R. PM and QN are perpendicular from P and Q on the x-axis Find:

(i) the ratio PR : RQ

(ii) the coordinates of R.

(iii) the area of the quadrilateral PMNQ.

The line joining P(-4, 5) and Q(3, 2) intersects the y-axis at point R. PM and QN are perpendicular from P and Q on the x-axis Find:

(i) the ratio PR : RQ

(ii) the coordinates of R.

(iii) the area of the quadrilateral PMNQ.

In the given figure line APB meets the x-axis at point A and y-axis at point B. P is the point (-4,2) and AP : PB = 1 : 2. Find the co-ordinates of A and B.

In the given figure line APB meets the x-axis at point A and y-axis at point B. P is the point (-4,2) and AP : PB = 1 : 2. Find the co-ordinates of A and B.

Given a line segment AB joining the points A (-4, 6) and B (8, -3). Find:
(i) the ratio in which AB is divided by the y-axis
(ii) find the coordinates of the point of intersection
(iii) the length of AB.

Given a line segment AB joining the points A (-4, 6) and B (8, -3). Find:
(i) the ratio in which AB is divided by the y-axis
(ii) find the coordinates of the point of intersection
(iii) the length of AB.

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Find the mid – point of the line segment joining the point: (-6, 7) and (3, 5)

Find the mid – point of the line segment joining the point: (-6, 7) and (3, 5)

Find the slope of the line whose inclination is: 0º

Find the slope of the line whose inclination is: 30°

Find the mid – point of the line segment joining the point: (5, -3) and (-1, 7)

Find the mid – point of the line segment joining the point: (5, -3) and (-1, 7)

Find the slope of the line whose inclination is: 72° 30'

Find the slope of the line whose inclination is: 46°

Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid point of AB is (2, 3). Find the values of x and y.

Points A and B have co-ordinates (3, 5) and (x, y) respectively. The mid point of AB is (2, 3). Find the values of x and y.

Find the inclination of the line whose slope is: 0

Find the inclination of the line whose slope is: sqrt3

Find the inclination of the line whose slope is: 0.7646

Find the inclination of the line whose slope is: 1.0875

A (5, 3), B(-1, 1) and C(7, -3) are the vertices of triangle ABC. If L is the mid-point of AB and M is the mid-point of AC, show that LM =1/2BC

A (5, 3), B(-1, 1) and C(7, -3) are the vertices of triangle ABC. If L is the mid-point of AB and M is the mid-point of AC, show that LM =1/2BC

Find the slope of the line passing through the (−2, −3) and (1, 2)

Find the slope of the line passing through the (−4, 0) and origin

Find the slope of the line passing through the (a, −b) and (b, −a)

Given M is the mid point of AB, find the co-ordinates of: A; if M = (1, 7) and B = (-5, 10)

Find the slope of the line parallel to AB if: A = (−2, 4) and B = (0, 6)

Given M is the mid point of AB, find the co-ordinates of: A; if M = (1, 7) and B = (-5, 10)

Find the slope of the line parallel to AB if: A = (0, −3) and B = (−2, 5)

Given M is the mid point of AB, find the co-ordinates of: B; if A = (3, -1) and M = (-1, 3)

Given M is the mid point of AB, find the co-ordinates of: B; if A = (3, -1) and M = (-1, 3)

P (-3, 2) is the mid-point of line segment AB as shown in the given figure. Find the co-ordinates of points A and B.

P (-3, 2) is the mid-point of line segment AB as shown in the given figure. Find the co-ordinates of points A and B.

Find the slope of the line perpendicular to AB if: A = (0, −5) and B = (−2, 4)

Find the slope of the line perpendicular to AB if: A = (3, −2) and B = (−1, 2)

In the given figure, P (4, 2) is mid-point of line segment AB. Find the co-ordinates of A and B.

In the given figure, P (4, 2) is mid-point of line segment AB. Find the co-ordinates of A and B.

The line passing through (0, 2) and (−3, −1) is parallel to the line passing through (-1, 5) and (4,a), Find a.

The line passing through (−4, −2) and (2, −3) is perpendicular to the line passing through (a, 5) and (2, −1). Find a.

(-5, 2), (3, -6) and (7, 4) are the vertices of a triangle. Find the length of its median through the vertex (3, -6)

(-5, 2), (3, -6) and (7, 4) are the vertices of a triangle. Find the length of its median through the vertex (3, -6)

Given a line ABCD in which AB = BC = CD, B= (0, 3) and C = (1, 8)
Find the co-ordinates of A and D.

Given a line ABCD in which AB = BC = CD, B= (0, 3) and C = (1, 8)
Find the co-ordinates of A and D.

Without using the distance formula, show that the points A (4, −2), B (−4, 4) and C (10, 6) are the vertices of a right angled triangle.

Without using the distance formula, show that the points A (4, 5), B (1, 2), C (4, 3) and D (7, 6) are the vertices of a parallelogram.

One end of the diameter of a circle is (-2, 5). Find the co-ordinates of the other end of it, of the centre of the circle is (2, -1)

One end of the diameter of a circle is (-2, 5). Find the co-ordinates of the other end of it, of the centre of the circle is (2, -1)

A (2, 5), B (1, 0), C (-4, 3) and D (-3, 8) are the vertices of quadrilateral ABCD. Find the coordinates of the mid-points of AC and BD. Give a special name to the quadrilateral.

(−2, 4), B (4, 8), C (10, 7) and D (11, -5) are the vertices of a quadrilateral. Show that the quadrilateral, obtained on joining the mid-points of its sides, is a parallelogram.

The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis. ∠A = 60° and vertex C = (7, 5). Find the equations of BC and CD.

A (2, 5), B (1, 0), C (-4, 3) and D (-3, 8) are the vertices of quadrilateral ABCD. Find the coordinates of the mid-points of AC and BD. Give a special name to the quadrilateral.

P (4, 2) and Q (-1, 5) are the vertices of parallelogram PQRS and (-3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.

Show that the points P (a, b + c), Q (b, c + a) and R (c, a + b) are collinear.

Find the equation of the straight line passing through origin and the point of intersection of the lines x + 2y = 7 and x – y = 4.

P (4, 2) and Q (-1, 5) are the vertices of parallelogram PQRS and (-3, 2) are the co-ordinates of the point of intersection of its diagonals. Find co-ordinates of R and S.

A (-1, 0), B (1, 3) and D (3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C.

A (-1, 0), B (1, 3) and D (3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C.

Find x, if the slope of the line joining (x, 2) and (8, −11) is −3/4

In triangle ABC, the co-ordinates of vertices A, B and C are (4, 7), (-2, 3) and (0, 1) respectively.
Find the equation of median through vertex A.
Also, find the equation of the line through vertex B and parallel to AC.

The side AB of an equilateral triangle ABC is parallel to the x-axis. Find the slopes of all its sides.

The points (2, -1), (-1, 4) and (-2, 2) are mid points of the sides of a triangle. Find its vertices

A, B and C have co-ordinates (0, 3), (4, 4) and (8, 0) respectively. Find the equation of the line through A and perpendicular to BC.

The points (2, -1), (-1, 4) and (-2, 2) are mid points of the sides of a triangle. Find its vertices

Points A (-5, x), B (y, 7) and C (1, -3) are collinear (i.e. lie on the same straight line) such that AB = BC. Calculate the values of x and y.

Find the equation of the perpendicular dropped from the point (−1, 2) onto the line joining the points (1, 4) and (2, 3)

Points A (-5, x), B (y, 7) and C (1, -3) are collinear (i.e. lie on the same straight line) such that AB = BC. Calculate the values of x and y.

The side AB of a square ABCD is parallel to x-axis. Find the slopes of all its sides. Also, find:
(i) the slope of the diagonal AC.
(ii) the slope of the diagonal BD.

Points P (a, −4), Q (−2, b) and R (0, 2) are collinear. If Q lies between P and R, such that PR = 2QR, calculate the values of a and b.

Points P (a, −4), Q (−2, b) and R (0, 2) are collinear. If Q lies between P and R, such that PR = 2QR, calculate the values of a and b.

A (5, 4), B (−3, −2) and C (1, −8) are the vertices of a triangle ABC. Find:
(i) the slope of the altitude of AB.
(ii) the slope of the median AD and
(iii) the slope of the line parallel to AC.

Find the equation of the line, whose x-intercept = 5 and y-intercept = 3

Find the equation of the line, whose x-intercept = -4 and y-intercept = 6

Find the equation of the line, whose  x-intercept = −8 and y-intercept = -4

The slope of the side BC of a rectangle ABCD is 2/3
Find:
(i) the slope of the side AB.
(ii) the slope of the side AD.

Find the equation of the line whose slope is -5/6 and x-intercept is 6.

Calculate the co-ordinates of the centroid of the triangle ABC, if A = (7, -2), B = (0, 1) and C =(-1, 4).

Calculate the co-ordinates of the centroid of the triangle ABC, if A = (7, -2), B = (0, 1) and C =(-1, 4).

The co-ordinates of the centroid of a triangle PQR are (2, -5). If Q = (-6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.

The co-ordinates of the centroid of a triangle PQR are (2, -5). If Q = (-6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.

Find the equation of the line with x-intercept 5 and a point on it (-3, 2)

Find the slope and the inclination of the line AB if:
(i) A = (−3, −2) and B = (1, 2)
(ii) A = (0, - sqrt3 ) and B = (3, 0)
(iii) A = (−1, 2sqrt3 ) and B = (−2, sqrt3 )

A (5, x), B (-4, 3) and C (y, -2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.

The points (−3, 2), (2, −1) and (a, 4) are collinear Find a.

Find the equations of the line through (1, 3) and making an intercept of 5 on the y-axis.

A (5, x), B (-4, 3) and C (y, -2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.

The points (K, 3), (2, −4) and (-K + 1, −2) are collinear. Find K.

Find the equations of the lines passing through point (-2, 0) and equally inclined to the coordinate axes.

Plot the points A (1, 1), B (4, 7) and C(4, 10) on a graph paper. Connect A and B and also A and C.
Which segment appears to have the steeper slope, AB or AC?
Justify your conclusion by calculating the slopes of AB and AC.

The line through P (5, 3) intersects y-axis at Q.
write the slope of the line

The line through P (5, 3) intersects y-axis at Q.
write the equation of the line

The line through P (5, 3) intersects y-axis at Q.

Find the co-ordinates of Q.

Write down the equation of the line whose gradient is -2/5 and which passes through point P, where P divides the line segement joining A(4, −8) and B (12, 0) in the ratio 3 : 1

Find the value(s) of k so that PQ will be parallel to RS. Given: P (2, 4), Q (3, 6), R (8, 1) and S (10, k)

Find the value(s) of k so that PQ will be parallel to RS. Given: P (3, −1), Q (7, 11), R (−1, −1) and S (1, k)

Find the value(s) of k so that PQ will be parallel to RS. Given: P (5, −1), Q (6, 11), R (6, −4k) and S (7, k2)

A (1, 4), B (3, 2) and C (7, 5) are vertices of a triangle ABC. Find the co-ordinates of the centroid of triangle ABC

A (1, 4), B (3, 2) and C (7, 5) are vertices of a triangle ABC. Find the equation of a line, through the centroid and parallel to AB.

A (7, −1), B (4, 1) and C (−3, 4) are the vertices of a triangle ABC. Find the equation of a line through the vertex B and the point P in AC; such that AP : CP = 2 : 3.

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Given a triangle ABC in which A = (4, -4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2, Find the length of line segment AP.

Given a triangle ABC in which A = (4, -4), B = (0, 5) and C = (5, 10). A point P lies on BC such that BP : PC = 3 : 2, Find the length of line segment AP.

Find the equation of a line whose:
y- intercept = 2 and slope = 3

A(20, 0) and B(10, -20) are two fixed points Find the co-ordinates of the point P in AB such that : 3PB = AB, Also, find the co-ordinates of some other point Q in AB such that AB = 6 AQ.

Find the equation of a line whose:
y – intercept = −1 and inclination = 45°

A(20, 0) and B(10, -20) are two fixed points Find the co-ordinates of the point P in AB such that : 3PB = AB, Also, find the co-ordinates of some other point Q in AB such that AB = 6 AQ.

Find the equation of the line whose slope is − 4/3 and which passes through (−3, 4)

A(-8, 0), B(0, 16) and C(0, 0) are the verticals of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5

Show that : PQ =3/8 BC

A(-8, 0), B(0, 16) and C(0, 0) are the verticals of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5

Show that : PQ =3/8 BC

Find the co-ordinates of points of trisection of the line segment joining the point (6, -9) and the origin.

Find the co-ordinates of points of trisection of the line segment joining the point (6, -9) and the origin.

Find the equation of a line which passes through (5, 4) and makes an angle of 60° with the positive direction of the x-axis.

A line segment joining A(-1,5/3) and B (a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects the y-axis.

(i) calculate the value of ‘a’
(ii) Calculate the co-ordinates of ‘P’.

A line segment joining A(-1,5/3) and B (a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects the y-axis.

(i) calculate the value of ‘a’
(ii) Calculate the co-ordinates of ‘P’.

Find the equation of the line passing through:  (0, 1) and (1, 2)

Find the equation of the line passing through: (−1, −4) and (3, 0)

In what ratio is the line joining A(0, 3) and B (4, -1) divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis

In what ratio is the line joining A(0, 3) and B (4, -1) divided by the x-axis? Write the co-ordinates of the point where AB intersects the x-axis

The co-ordinates of two points P and Q are (2, 6) and (−3, 5) respectively Find the gradient of PQ;

The co-ordinates of two points P and Q are (2, 6) and (−3, 5) respectively Find the equation of PQ;

The co-ordinates of two points P and Q are (2, 6) and (−3, 5) respectively Find the co-ordinates of the point where PQ intersects the x-axis.

The mid-point of the segment AB, as shown in diagram, is C(4, -3). Write down the co-ordinates of A and B.

The mid-point of the segment AB, as shown in diagram, is C(4, -3). Write down the co-ordinates of A and B.

The co-ordinates of two points A and B are (-3, 4) and (2, -1) Find the equation of AB

The co-ordinates of two points A and B are (-3, 4) and (2, -1) Find: the co-ordinates of the point where the line AB intersects the y-axis.

The figure given alongside shows two straight lines AB and CD intersecting each other at point P (3, 4). Find the equations of AB and CD.

AB is a diameter of a circle with centre C = (-2, 5). If A = (3, -7), find
(i) the length of radius AC
(ii) the coordinates of B.

AB is a diameter of a circle with centre C = (-2, 5). If A = (3, -7), find
(i) the length of radius AC
(ii) the coordinates of B.

Find the co-ordinates of the centroid of a triangle ABC whose vertices are: A(-1, 3), B(1, -1) and C(5, 1)

Find the co-ordinates of the centroid of a triangle ABC whose vertices are: A(-1, 3), B(1, -1) and C(5, 1)

The mid point of the line segment joining (4a, 2b -3) and (-4, 3b) is (2, -2a). Find the values of a and b.

The mid point of the line segment joining (4a, 2b -3) and (-4, 3b) is (2, -2a). Find the values of a and b.

The mid point of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a + 1). Find the values of a and b.

The mid point of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a + 1). Find the values of a and b.

(i) write down the co-ordinates of the point P that divides the line joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.
(ii) Calculate the distance OP, where O is the origin.
(iii) In what ratio does the Y-axis divide the line AB?

(i) write down the co-ordinates of the point P that divides the line joining A(-4, 1) and B(17, 10) in the ratio 1 : 2.
(ii) Calculate the distance OP, where O is the origin.
(iii) In what ratio does the Y-axis divide the line AB?

Prove that the points A(-5, 4); B(-1, -2) and C(5, 2) are the vertices of an isosceles right angled triangle. Find the co-ordinates of D so that ABCD is a square.

Prove that the points A(-5, 4); B(-1, -2) and C(5, 2) are the vertices of an isosceles right angled triangle. Find the co-ordinates of D so that ABCD is a square.

M is the mid-point of the line segment joining the points A(-3, 7) and B(9, -1). Find the coordinates of point M. Further, if R(2, 2) divides the line segment joining M and the origin in the ratio p : q, find the ratio p : q

M is the mid-point of the line segment joining the points A(-3, 7) and B(9, -1). Find the coordinates of point M. Further, if R(2, 2) divides the line segment joining M and the origin in the ratio p : q, find the ratio p : q

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Given 3x + 2y + 4 = 0
(i) express the equation in the form y = mx + c
(ii) Find the slope and y-intercept of the line 3x + 2y + 4 = 0

Find the slope and y-intercept of the line: y = 4

Find the slope and y-intercept of the line: ax – by = 0

Find the slope and y-intercept of the line: 3x – 4y = 5

The equation of a line is x – y = 4. Find its slope and y – intercept. Also, find its inclination.

Is the line 3x + 4y + 7 = 0 perpendicular to the line 28x – 21y + 50 = 0?

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