#### Chapters

#### Balbharati SSC Class 10 Mathematics 2

## Chapter 5 : Co-ordinate Geometry

#### Pages 107 - 108

Find the distance between the following pair of point.

A(2, 3), B(4, 1)

Find the distance between the following pair of point.

P(–5, 7), Q(–1, 3)

Find the distance between the following pair of point.

\[R\left( 0, - 3 \right), S\left( 0, \frac{5}{2} \right)\].

Find the distance between each of the following pairs of points.

L(5, –8), M(–7, –3)

Find the distance between the following pair of point.

T(–3, 6), R(9, –10)

Find the distance between the following pair of point.

\[W\left( \frac{- 7}{2} , 4 \right), X\left( 11, 4 \right)\]

Determine whether the point is collinear.

A(1, –3), B(2, –5), C(–4, 7)

Determine whether the point is collinear.

L(–2, 3), M(1, –3), N(5, 4)

Determine whether the point is collinear.

R(0, 3), D(2, 1), S(3, –1)

Determine whether the point is collinear.

P(–2, 3), Q(1, 2), R(4, 1)

Find the point on the X–axis which is equidistant from A(–3, 4) and B(1, –4).

Verify that points P(–2, 2), Q(2, 2) and R(2, 7) are vertices of a right angled triangle.

Show that points P(2, –2), Q(7, 3), R(11, –1) and S (6, –6) are vertices of a parallelogram.

Show that points A(–4, –7), B(–1, 2), C(8, 5) and D(5, –4) are vertices of a rhombus ABCD.

Find *x* if distance between points L(*x*, 7) and M(1, 15) is 10.

Show that the points A(1, 2), B(1, 6), \[C\left( 1 + 2\sqrt{3}, 4 \right)\] are vertices of an equilateral triangle.

#### Pages 115 - 116

Find the coordinates of point P if P divides the line segment joining the points A(–1,7) and B(4,–3) in the ratio 2 : 3.

In the following example find the co-ordinate of point A which divides segment PQ in the ratio *a *: *b*.

P(–3, 7), Q(1, –4), *a *: *b *= 2 : 1

In the following example find the co-ordinate of point A which divides segment PQ in the ratio *a *: *b*.

P(–2, –5), Q(4, 3), *a *: *b *= 3 : 4

In the following example find the co-ordinate of point A which divides segment PQ in the ratio *a *: *b*.

P(2, 6), Q(–4, 1), *a *: *b *= 1 : 2

Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8).

Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.

Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k ?

Find the coordinates of midpoint of the segment joining the points (22, 20) and (0, 16).

Find the centroid of the triangle whose vertice is given below.

(–7, 6), (2, –2), (8, 5)

Find the centroid of the triangle whose vertice is given below.

(3, –5), (4, 3), (11, –4)

Find the centroid of the triangle whose vertice is given below.

(4, 7), (8, 4), (7, 11)

In ∆ABC, G (–4, –7) is the centroid. If A (–14, –19) and B(3, 5) then find the co–ordinates of C.

A(h, –6), B(2, 3) and C(–6, k) are the co–ordinates of vertices of a triangle whose centroid is G (1, 5). Find h and k.

Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7) and B(–4, –8).

If A (–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.

If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

#### Pages 121 - 122

Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.

45°

Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.

60°

Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.

90°

Find the slope of the lines passing through the given point.

A (2, 3) , B (4, 7)

Find the slope of the lines passing through the given point.

P (–3, 1) , Q (5, –2)

Find the slope of the lines passing through the given point.

C (5, –2) , ∆ (7, 3)

Find the slope of the lines passing through the given point.

L (–2, –3) , M (–6, –8)

Find the slope of the lines passing through the given point.

E(–4, –2) , F (6, 3)

Find the slope of the lines passing through the given point.

T (0, –3) , S (0, 4)

Determine whether the following point is collinear.

A(–1, –1), B(0, 1), C(1, 3)

Determine whether the following point is collinear.

D(–2, –3), E(1, 0), F(2, 1)

Determine whether the following point is collinear.

L(2, 5), M(3, 3), N(5, 1)

Determine whether the following point is collinear.

P(2, –5), Q(1, –3), R(–2, 3)

Determine whether the following point is collinear.

R(1, –4), S(–2, 2), T(–3, 4)

Determine whether the following point is collinear.

A(–4, 4), \[K\left( - 2, \frac{5}{2} \right),\] N (4, –2)

If A (1, –1), B (0, 4), C (–5, 3) are vertices of a triangle then find the slope of each side.

Show that A(–4, –7), B (–1, 2), C (8, 5) and D (5, –4) are the vertices of a parallelogram.

Find *k, *if R(1, –1), S (–2, *k*) and slope of line RS is –2.

Find *k*, if B(*k*, –5), C (1, 2) and slope of the line is 7.

Find *k*, if PQ || RS and P(2, 4), Q (3, 6), R(3, 1), S(5, *k*).

#### Pages 122 - 123

Fill in the blank using correct alternative.

Seg AB is parallel to Y-axis and coordinates of point A are (1,3) then co–ordinates of point B can be ........ .

(A) (3,1)

(B) (5,3)

(C) (3,0)

(D) (1,–3)

Fill in the blank using correct alternative.

Out of the following, point ........ lies to the right of the origin on X– axis.

(A) (–2,0)

(B) (0,2)

(C) (2,3)

(D) (2,0)

Fill in the blank using correct alternative.

Distance of point (–3,4) from the origin is ...... .

(A) 7

(B) 1

(C) 5

(D) –5

Fill in the blank using correct alternative.

A line makes an angle of 30° with the positive direction of X– axis. So the slope of the line is .......... .

(A)\[\frac{1}{2}\]

(B) \[\frac{\sqrt{3}}{2}\]

(C) \[\frac{1}{\sqrt{3}}\]

(D) \[\sqrt{3}\]

Determine whether the given point is collinear.

A(0,2), B(1,–0.5), C(2,–3)

Determine whether the given point is collinear.

\[P\left( 1, 2 \right), Q\left( 2, \frac{8}{5} \right), R\left( 3, \frac{6}{5} \right)\]

Determine whether the given point is collinear.

L(1,2), M(5,3) , N(8,6)

Find the coordinates of the midpoint of the line segment joining P(0,6) and Q(12,20).

Find the ratio in which the line segment joining the points A(3,8) and B(–9, 3) is divided by the Y– axis.

Find the point on X–axis which is equidistant from P(2,–5) and Q(–2,9).

Find the distances between the following point.

A(*a*, 0), B(0, *a*)

Find the distances between the following point.

P(–6, –3), Q(–1, 9)

Find the distances between the following point.

R(–3*a*, *a*), S(*a*, –2*a*)

Find the coordinates of the circumcentre of a triangle whose vertices are (–3,1), (0,–2) and (1,3).

In the following example, can the segment joining the given point form a triangle ? If triangle is formed, state the type of the triangle considering side of the triangle.

L(6,4) , M(–5,–3) , N(–6,8)

In the following example, can the segment joining the given point form a triangle ? If triangle is formed, state the type of the triangle considering side of the triangle.

P(–2,–6) , Q(–4,–2), R(–5,0)

In the following example, can the segment joining the given point form a triangle ? If triangle is formed, state the type of the triangle considering side of the triangle.

\[A\left( \sqrt{2} , \sqrt{2} \right), B\left(-\sqrt{2} , -\sqrt{2} \right), C\left( -\sqrt{6} , \sqrt{6} \right)\]

Find *k *if the line passing through points P(–12, –3) and Q(4, *k*) has slope \[\frac{1}{2}\].

Show that the line joining the points A(4, 8) and B(5, 5) is parallel to the line joining the points C(2, 4) and D(1, 7).

Show that points P(1, –2), Q(5, 2), R(3, –1), S(–1, –5) are the vertices of a parallelogram.

Show that the ▢PQRS formed by P(2, 1), Q(–1, 3), R(–5, –3) and S(–2, –5) is a rectangle .

Find the lengths of the medians of a triangle whose vertices are A(–1, 1), B(5, –3) and C(3, 5).

Find the coordinates of centroid of the triangles if points D(–7, 6), E(8, 5) and F(2, –2) are the mid points of the sides of that triangle.

Show that A(4, –1), B(6, 0), C(7, –2) and D(5, –3) are vertices of a square.

Find the coordinates of circumcentre and radius of circumcircle of ∆ABC if A(7, 1), B(3, 5) and C(2, 0) are given.

Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.

Find the type of the quadrilateral if points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) are joined serially.

The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.

Find the coordinates of the centre of the circle passing through the points P(6, –6), Q(3, –7) and R (3, 3).

Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2).

Find the slope of the diagonals of a quadrilateral with vertices A(1, 7), B(6, 3), C(0, –3) and D(–3, 3).

#### Balbharati SSC Class 10 Mathematics 2

#### Textbook solutions for Class 10th Board Exam

## Balbharati solutions for Class 10th Board Exam Geometry chapter 5 - Co-ordinate Geometry

Balbharati solutions for Class 10th Board Exam Geometry chapter 5 (Co-ordinate Geometry) 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 Maharashtra State Board Textbook for SSC Class 10 Mathematics 2 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 10th Board Exam Geometry chapter 5 Co-ordinate Geometry are Centroid Formula, Co-ordinates of the Midpoint of a Segment, Section Formula, Division of a Line Segment, Distance Formula, Concepts of Coordinate Geometry, General Equation of a Line, Standard Forms of Equation of a Line, Intercepts Made by a Line, Slope of a Line.

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