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# Frank solutions for Class 10 Maths chapter 12 - Distance and Section Formulae

## Chapter 12: Distance and Section Formulae

Exercise 12.1Exercise 12.2Exercise 12.3

#### Frank solutions for Class 10 Maths Chapter 12 Exercise Exercise 12.1 [Page 0]

Find the distance between the following pair of point in the coordinate plane :

(5 , -2) and (1 , 5)

Find the distance between the following pair of point in the coordinate plane.

(1 , 3) and (3 , 9)

Find the distance between the following pairs of point in the coordinate plane :

(7 , -7) and (2 , 5)

Find the distance between the following pairs of point in the coordinate plane :

(4 , 1) and (-4 , 5)

Find the distance between the following pairs of point in the coordinate plane :

(13 , 7) and (4 , -5)

Find the relation between x and y if the point M (x,y) is equidistant from R (0,9) and T (14 , 11).

Find the distance between P and Q if P lies on the y - axis and has an ordinate 5 while Q lies on the x - axis and has an abscissa 12 .

P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.

Find the point on the x-axis equidistant from the points (5,4) and (-2,3).

A line segment of length 10 units has one end at A (-4 , 3). If the ordinate of te othyer end B is 9 , find the abscissa of this end.

Prove that the following set of point is collinear :

(5 , 5),(3 , 4),(-7 , -1)

Prove that the following set of point is collinear :

(5 , 1),(3 , 2),(1 , 3)

Prove that the following set of point is collinear :

(4, -5),(1 , 1),(-2 , 7)

Find the coordinate of O , the centre of a circle passing through A (8 , 12) , B (11 , 3), and C (0 , 14). Also , find its radius.

Find the coordinate of O , the centre of a circle passing through P (3 , 0), Q (2 , sqrt 5) and R (-2 sqrt 2 , -1). Also find its radius.

Find the coordinates of O, the centre passing through A( -2, -3), B(-1, 0) and C(7, 6). Also, find its radius.

The centre of a circle passing through P(8, 5) is (x+l , x-4). Find the coordinates of the centre if the diameter of the circle is 20 units.

Find the distance of the following point from the origin :

(5 , 12)

Find the distance of the following point from the origin :

(6 , 8)

Find the distance of the following point from the origin :

(8 , 15)

Find the distance of the following point from the origin :

(0 , 11)

Find the distance of the following point from the origin :

(13 , 0)

A(-2, -3), B(-1, 0) and C(7, -6) are the vertices of a triangle. Find the circumcentre and the circumradius of the triangle.

P(5 , -8) , Q (2 , -9) and R(2 , 1) are the vertices of a triangle. Find tyhe circumcentre and the circumradius of the triangle.

x (1,2),Y (3, -4) and z (5,-6) are the vertices of a triangle . Find the circumcentre and the circumradius of the triangle.

Prove that the points (6 , -1) , (5 , 8) and (1 , 3) are the vertices of an isosceles triangle.

Prove that the points (1 ,1),(-4 , 4) and (4 , 6) are the certices of an isosceles triangle.

Prove taht the points (-2 , 1) , (-1 , 4) and (0 , 3) are the vertices of a right - angled triangle.

Prove that the points (7 , 10) , (-2 , 5) and (3 , -4) are vertices of an isosceles right angled triangle.

Prove that the points (1 , 1) , (-1 , -1) and (- sqrt 3 , sqrt 3) are the vertices of an equilateral triangle.

Prove that the points (0,3) , (4,3) and (2, 3+2sqrt 3) are the vertices of an equilateral triangle.

Prove that the points (5 , 3) , (1 , 2), (2 , -2) and (6 ,-1) are the vertices of a square.

Find the distance between the following point :

(p+q,p-q) and (p-q, p-q)

Find the distance between the following point :

(sin θ , cos θ) and (cos θ , - sin θ)

Find the distance between the following point :

(sec θ , tan θ) and (- tan θ , sec θ)

Find the distance between the following point :

(Sin θ - cosec θ , cos θ - cot θ) and (cos θ - cosec θ , -sin θ - cot θ)

Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.

Prove that the points (0 , 0) , (3 , 2) , (7 , 7) and (4 , 5) are the vertices of a parallelogram.

Prove that the points (0 , 2) , (1 , 1) , (4 , 4) and (3 , 5) are the vertices of a rectangle.

Prove that the points (a , b) , (a + 3 , b + 4) , (a - 1 , b + 7) and (a - 4 , b + 3) are the vertices of a parallelogram.

Prove that the points (0 , -4) , (6 , 2) , (3 , 5) and (-3 , -1) are the vertices of a rectangle.

ABCD is a square . If the coordinates of A and C are (5 , 4) and (-1 , 6) ; find the coordinates of B and D.

PQR  is an isosceles triangle . If two of its vertices are P (2 , 0) and Q (2 , 5) , find the coordinates of R if the length of each of the two equal sides is 3.

ABC is an equilateral triangle . If the coordinates of A and B are (1 , 1) and (- 1 , -1) , find the coordinates of C.

Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.

Find the distance of a point (13 , -9) from another point on the line y = 0 whose abscissa is 1.

Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.

Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .

Find the value of m if the distance between the points (m , -4) and (3 , 2) is 3sqrt 5 units.

Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).

#### Frank solutions for Class 10 Maths Chapter 12 Exercise Exercise 12.2 [Page 0]

Find the coordinate of a point P which divides the line segment joining :

A (3, -3) and B (6, 9) in the ratio 1 :2.

Find the coordinate of a point P which divides the line segment joining :

M( -4, -5) and N (3, 2) in the ratio 2 : 5.

Find the coordinate of a point P which divides the line segment joining :

5(2, 6) and R(9, -8) in the ratio 3: 4.

Find the coordinate of a point P which divides the line segment joining :

D(-7, 9) and E( 15, -2) in the ratio 4:7.

Find the coordinate of a point P which divides the line segment joining :

A(-8, -5) and B (7, 10) in the ratio 2:3.

In what ratio is the line joining (2, -4) and (-3, 6) divided by the line y = O ?

Find the ratio in which the line x = O divides the join of ( -4, 7) and (3, 0).
Also, find the coordinates of the point of intersection.

(4, 2) and (-1, 5) are the adjacent vertices ofa parallelogram. (-3, 2) are the coordinates of the points of intersection of its diagonals. Find the coordinates of the other two vertices.

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

Find the coordinates of point P which divides line segment joining A ( 3, -10) and B (3, 2) in such a way that PB: AB= 1.5.

Find the ratio in which the line x = -2 divides the line segment joining (-6, -1) and (1, 6). Find the coordinates of the point of intersection.

Find the ratio in which the line y = -1 divides the line segment joining (6, 5) and (-2, -11). Find the coordinates of the point of intersection.

The line joining P (-5, 6) and Q (3, 2) intersects the y-axis at R. PM and QN are perpendiculars from P and Q on the x-axis. Find the ratio PR: RQ.

B is a point on the line segment AC. The coordinates of A and B are (2, 5) and (1, 0). If AC= 3 AB, find the coordinates of C.

Q is a point on the line segment AB. The coordinates of A and B are (2, 7) and (7, 12) along the line AB so that AQ = 4BQ. Find the coordinates of Q.

The origin o (0, O), P (-6, 9) and Q (12, -3) are vertices of triangle OPQ. Point M divides OP in the ratio 1: 2 and point N divides OQ in the ratio 1: 2. Find the coordinates of points M and N. Also, show that 3MN = PQ.

Find the points of trisection of the segment joining A ( -3, 7) and B (3, -2).

A (2, 5), B (-1, 2) and C (5, 8) are the vertices of triangle ABC. Point P and Q lie on AB and AC respectively, such that AP: PB = AQ: QC = 1: 2. Calculate the coordinates of P and Q. Also, show that 3PQ = BC.

A (30, 20) and B ( 6, -4) are two fixed points. Find the coordinates of a point Pin AB such that 2PB = AP. Also, find the coordinates of some other point Qin AB such that AB = 6 AQ.

Show that the line segment joining the points (-3, 10) and (6, -5) is trisected by the coordinates axis.

Show that the lines x = O and y = O trisect the line segment formed by joining the points (-10, -4) and (5, 8). Find the points of trisection.

Find the coordinates of the points of trisection of the line segment joining the points (3, -3) and ( 6, 9).

Find the ratio in which the point P (2, 4) divides the line joining points (-3, 1) and (7, 6).

Find the ratio in which the point R ( 1, 5) divides the line segment joining the points S (-2, -1) and T (5, 13).

The points A, B and C divides the line segment MN in four equal parts. The coordinates of Mand N are (-1, 10) and (7, -2) respectively. Find the coordinates of A, B and C.

Find the ratio in which the line segment joining A (2, -3) and B(S, 6) i~ divided by the x-axis.

Find the ratio in which the line segment joining P ( 4, -6) and Q ( -3, 8) is divided by the line y = 0.

In what ratio is the line joining (2, -1) and (-5, 6) divided by the y axis ?

#### Frank solutions for Class 10 Maths Chapter 12 Exercise Exercise 12.3 [Page 0]

Find the midpoint of the line segment joining the following pair of point :

(4,7) and (10,15)

Find the midpoint of the line segment joining the following pair of point :

( -3, 5) and (9, -9)

Find the midpoint of the line segment joining the following pair of point :

(a+b, b-a) and (a-b, a+b)

Find the midpoint of the line segment joining the following pair of point :

(3a-2b, Sa+7b) and (a+4b, a-3b)

Find the midpoint of the line segment joining the following pair of point :

( a+3, 5b), (3a-1, 3b +4).

A(6, -2), B(3, -2) and C(S, 6) are the three vertices of a parallelogram ABCD. Find the coordinates of the fourth vertex c.

P( -2, 5), Q(3, 6 ), R( -4, 3) and S(-9, 2) are the vertices of a quadrilateral. Find the coordinates of the midpoints of the diagonals PR and QS. Give a special name to the quadrilateral.

Three consecutive vertices of a parallelogram ABCD are A(S, 5), B(-7, -5) and C(-5, 5). Find the coordinates of the fourth vertex D.

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

If the midpoints of the sides ofa triangle are (-2, 3), (4, -3), (4, 5), find its vertices.

If (-3, 2), (1, -2) and (5, 6) are the midpoints of the sides of a triangle, find the coordinates of the vertices of the triangle.

Find the length of the median through the vertex A of triangle ABC whose vertices are A (7, -3), B(S, 3) and C(3, -1).

Find the centroid of a triangle whose vertices are (3, -5), (-7, 4) and ( 10, -2).

Two vertices of a triangle are (1, 4) and (3, 1). If the centroid of the triangle is the origin, find the third vertex.

The mid-point of the line segment joining A (- 2 , 0) and B (x , y) is P (6 , 3). Find the coordinates of B.

A( 4, 2), B(-2, -6) and C(l, 1) are the vertices of triangle ABC. Find its centroid and the length of the median through C.

A triangle is formed by line segments joining the points (5, 1 ), (3, 4) and (1, 1). Find the coordinates of the centroid.

The coordinates of the centroid I of triangle PQR are (2, 5). If Q = (-6, 5) and R = (7, 8). Calculate the coordinates of vertex P.

Two vertices of a triangle are ( -1, 4) and (5, 2). If the centroid is (0, 3), find the third vertex.

The midpoints of three sides of a triangle are (1, 2), (2, -3) and (3, 4). Find the centroid of the triangle.

ABC is a triangle whose vertices are A(-4, 2), B(O, 2) and C(-2, -4). D. E and Fare the midpoint of the sides BC, CA and AB respectively. Prove that the centroid of the  Δ ABC coincides with the centroid of the Δ DEF.

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

The centre of a circle is (a+2, a-1). Find the value of a, given that the circle passes through the points (2, -2) and (8, -2).

Let A(-a, 0), B(0, a) and C(α , β) be the vertices of the L1 ABC and G be its centroid . Prove that

GA2 + GB2 + GC2 = 1/3 (AB2 + BC2 + CA2)

A(2, 5), B(-2, 4) and C(-2, 6) are the vertices of a triangle ABC. Prove that ABC is an isosceles triangle.

A lies on the x - axis amd B lies on the y -axis . The midpoint of the line segment AB is (4 , -3). Find the coordinates of A and B .

P , Q and R are collinear points such that PQ = QR . IF the coordinates of P , Q and R are (-5 , x) , (y , 7) , (1 , -3) respectively, find the values of x and y.

A , B and C are collinear points such that AB = 1/2 AC . If the coordinates of A, B and C are (-4 , -4) , (-2 , b) anf (a , 2),Find the values of a and b.

The midpoint of the line segment joining the points P (2 , m) and Q (n , 4) is R (3 , 5) . Find the values of m and n.

The mid point of the line segment joining the points (p, 2) and (3, 6) is (2, q). Find the numerical values of a and b.

The coordinates of the end points of the diameter of a circle are (3, 1) and (7, 11). Find the coordinates of the centre of the circle.

AB is a diameter of a circle with centre 0. If the ooordinates of A and 0 are ( 1, 4) and (3, 6 ). Find the ooordinates of B and the length of the diameter.

## Chapter 12: Distance and Section Formulae

Exercise 12.1Exercise 12.2Exercise 12.3

## Frank solutions for Class 10 Mathematics chapter 12 - Distance and Section Formulae

Frank solutions for Class 10 Maths chapter 12 (Distance and Section Formulae) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Frank Class 10 Mathematics Part 2 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Frank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 12 Distance and Section Formulae are Co-ordinates Expressed as (x,y), Distance Formula, Section Formula, Mid-point Formula.

Using Frank Class 10 solutions Distance and Section Formulae exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Frank Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Frank Textbook Solutions to score more in exam.

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