#### Chapters

Chapter 2: Banking (Recurring Deposit Account)

Chapter 3: Shares and Dividend

Chapter 4: Linear Inequations (In one variable)

Chapter 5: Quadratic Equations

Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7: Ratio and Proportion (Including Properties and Uses)

Chapter 8: Remainder and Factor Theorems

Chapter 9: Matrices

Chapter 10: Arithmetic Progression

Chapter 11: Geometric Progression

Chapter 12: Reflection

Chapter 13: Section and Mid-Point Formula

Chapter 14: Equation of a Line

Chapter 15: Similarity (With Applications to Maps and Models)

Chapter 16: Loci (Locus and Its Constructions)

Chapter 17: Circles

Chapter 18: Tangents and Intersecting Chords

Chapter 19: Constructions (Circles)

Chapter 20: Cylinder, Cone and Sphere

Chapter 21: Trigonometrical Identities

Chapter 22: Height and Distances

Chapter 23: Graphical Representation

Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25: Probability

## Chapter 13: Section and Mid-Point Formula

#### Exercise 13(A) [Pages 177 - 178]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 13 Section and Mid-Point Formula Exercise 13(A) [Pages 177 - 178]

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 (-4, 6) and B(3, -5) in the ratio 3 : 2

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, -4) and (-3, 6) divided by the y – axis.

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 (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.

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.

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 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.

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.

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 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.

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

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

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?

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 (-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 (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.

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.

If P(-b, 9a - 2) divides the line segment joining the points A(-3, 3a + 1) and B(5, 8a) in the ratio 3: 1, find the values of a and b.

#### Exercise 13(B) [Page 182]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 13 Section and Mid-Point Formula Exercise 13(B) [Page 182]

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: (5, -3) and (-1, 7)

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.

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

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

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.

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

(-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.

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.

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.

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.

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.

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.

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.

#### Exercise 13(C) [Pages 182 - 183]

### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 13 Section and Mid-Point Formula Exercise 13(C) [Pages 182 - 183]

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.

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.

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.

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’.

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

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.

(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.

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

Calculate the ratio in which the line joining A(-4,2) and B(3,6) is divided by point p(x,3). Also, find x

Find the ratio in which the line `2x+y=4` divides th line segment joining the point` p(2,-2) and Q (3,7).`

If the abscissa of point P is 2. find the ratio in which this point divides the line segment joining the point `(-4,3) and (6,3)`. Also find the co-ordinates of point P.

The line joining the points (2,1) and (5,-8) is trisected at the point P and Q, point P lies on the line `2x-y+k=0`, find the value of k Also, find the co-ordinates of point Q.

Find the image of the point A(5,3) under reflection in the point P(-1,3).

M is the mid-point of the line segment joining the points A(0,4) and B(6,0). M also divides the line segment OP in the ratio 1:3 find :

(a) co-ordinates of M

(b) Co-ordinates of P

(C) Length Of BP

A (-4,2)2, B(0,2) and C (-2,-4) are the vertices of a triangle ABC. A,Q and R are mid-Points of sides BC,CA and AB respectively.Show that the centroid of Δ PQR is the same as the centroid of Δ ABC.

A(3, 1), B(y, 4) and C(1, x) are vertices of a triangle ABC. P, Q and R are mid - points of sides BC, CA and AB respectively. Show that the centroid of ΔPQR is the same as the centroid ΔABC.

## Chapter 13: Section and Mid-Point Formula

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

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Concepts covered in Concise Mathematics Class 10 ICSE chapter 13 Section and Mid-Point Formula are Co-ordinates Expressed as (x,y), Distance Formula, Section Formula, Mid-point Formula.

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