# Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board chapter 5 - Co-ordinate Geometry [Latest edition]

#### Chapters ## Chapter 5: Co-ordinate Geometry

Practice Set 5.1Practice Set 5.2Practice Set 5.3Problem Set 5
Practice Set 5.1 [Pages 107 - 108]

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 5 Co-ordinate Geometry Practice Set 5.1 [Pages 107 - 108]

Practice Set 5.1 | Q 1.1 | Page 107

Find the distance between the following pair of point.

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

Practice Set 5.1 | Q 1.2 | Page 107

Find the distance between the following pair of point.

P(–5, 7), Q(–1, 3)

Practice Set 5.1 | Q 1.3 | Page 107

Find the distance between the following pair of point.

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

Practice Set 5.1 | Q 1.4 | Page 107

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

L(5, –8), M(–7, –3)

Practice Set 5.1 | Q 1.5 | Page 107

Find the distance between the following pair of point.

T(–3, 6), R(9, –10)

Practice Set 5.1 | Q 1.6 | Page 107

Find the distance between the following pairs of point.

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

Practice Set 5.1 | Q 2.1 | Page 107

Determine whether the point is collinear.
A(1, –3), B(2, –5), C(–4, 7)

Practice Set 5.1 | Q 2.2 | Page 107

Determine whether the point is collinear.

L(–2, 3), M(1, –3), N(5, 4)

Practice Set 5.1 | Q 2.3 | Page 107

Determine whether the point is collinear.

R(0, 3), D(2, 1), S(3, –1)

Practice Set 5.1 | Q 2.4 | Page 107

Determine whether the point is collinear.

P(–2, 3), Q(1, 2), R(4, 1)

Practice Set 5.1 | Q 3 | Page 107

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

Practice Set 5.1 | Q 4 | Page 107

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

Practice Set 5.1 | Q 5 | Page 108

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

Practice Set 5.1 | Q 6 | Page 108

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

Practice Set 5.1 | Q 7 | Page 108

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

Practice Set 5.1 | Q 8 | Page 108

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

Practice Set 5.2 [Pages 115 - 116]

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 5 Co-ordinate Geometry Practice Set 5.2 [Pages 115 - 116]

Practice Set 5.2 | Q 1 | Page 115

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.

Practice Set 5.2 | Q 2.1 | Page 115

In the following example find the co-ordinate of point A which divides segment PQ in the ratio b.
P(–3, 7), Q(1, –4), = 2 : 1

Practice Set 5.2 | Q 2.2 | Page 115

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

Practice Set 5.2 | Q 2.3 | Page 115

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

P(2, 6), Q(–4, 1), = 1 : 2

Practice Set 5.2 | Q 3 | Page 115

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

Practice Set 5.2 | Q 4 | Page 115

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.

Practice Set 5.2 | Q 5 | Page 115

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

Practice Set 5.2 | Q 6 | Page 115

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

Practice Set 5.2 | Q 7.1 | Page 115

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

(–7, 6), (2, –2), (8, 5)

Practice Set 5.2 | Q 7.2 | Page 115

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

(3, –5), (4, 3), (11, –4)

Practice Set 5.2 | Q 7.3 | Page 115

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

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

Practice Set 5.2 | Q 8 | Page 116

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

Practice Set 5.2 | Q 9 | Page 116

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.

Practice Set 5.2 | Q 10 | Page 116

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

Practice Set 5.2 | Q 11 | Page 116

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

Practice Set 5.2 | Q 12 | Page 116

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

Practice Set 5.3 [Pages 121 - 122]

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 5 Co-ordinate Geometry Practice Set 5.3 [Pages 121 - 122]

Practice Set 5.3 | Q 1.1 | Page 121

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

45°

Practice Set 5.3 | Q 1.2 | Page 121

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

60°

Practice Set 5.3 | Q 1.3 | Page 121

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

90°

Practice Set 5.3 | Q 2.1 | Page 121

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

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

Practice Set 5.3 | Q 2.2 | Page 121

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

P (–3, 1) , Q (5, –2)

Practice Set 5.3 | Q 2.3 | Page 121

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

C (5, –2) , ∆ (7, 3)

Practice Set 5.3 | Q 2.4 | Page 121

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

L (–2, –3) , M (–6, –8)

Practice Set 5.3 | Q 2.5 | Page 121

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

E(–4, –2) , F (6, 3)

Practice Set 5.3 | Q 2.6 | Page 121

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

T (0, –3) , S (0, 4)

Practice Set 5.3 | Q 3.1 | Page 121

Determine whether the following point is collinear.
A(–1, –1), B(0, 1), C(1, 3)

Practice Set 5.3 | Q 3.2 | Page 121

Determine whether the following point is collinear.

D(–2, –3), E(1, 0), F(2, 1)

Practice Set 5.3 | Q 3.3 | Page 121

Determine whether the following point is collinear.

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

Practice Set 5.3 | Q 3.4 | Page 121

Determine whether the following point is collinear.

P(2, –5), Q(1, –3), R(–2, 3)

Practice Set 5.3 | Q 3.5 | Page 121

Determine whether the following point is collinear.

R(1, –4), S(–2, 2), T(–3, 4)

Practice Set 5.3 | Q 3.6 | Page 121

Determine whether the following point is collinear.

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

Practice Set 5.3 | Q 4 | Page 121

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

Practice Set 5.3 | Q 5 | Page 121

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

Practice Set 5.3 | Q 6 | Page 122

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

Practice Set 5.3 | Q 7 | Page 122

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

Practice Set 5.3 | Q 8 | Page 122

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

Problem Set 5 [Pages 122 - 123]

### Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board Chapter 5 Co-ordinate Geometry Problem Set 5 [Pages 122 - 123]

Problem Set 5 | Q 1.1 | Page 122

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 ........ .

• (3,1)

• (5,3)

• (3,0)

• (1,–3)

Problem Set 5 | Q 1.2 | Page 122

Fill in the blank using correct alternative.

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

• (–2,0)

• (0,2)

• (2,3)

• (2,0)

Problem Set 5 | Q 1.3 | Page 122

Fill in the blank using correct alternative.

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

• 7

• 1

• 5

• -5

Problem Set 5 | Q 1.4 | Page 122

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 .......... .

• $\frac{1}{2}$

• $\frac{\sqrt{3}}{2}$

• $\frac{1}{\sqrt{3}}$

• $\sqrt{3}$

Problem Set 5 | Q 2.1 | Page 122

Determine whether the given point is collinear.
A(0,2), B(1,–0.5), C(2,–3)

Problem Set 5 | Q 2.2 | Page 122

Determine whether the given point is collinear.

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

Problem Set 5 | Q 2.3 | Page 122

Determine whether the given point is collinear.

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

Problem Set 5 | Q 3 | Page 122

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

Problem Set 5 | Q 4 | Page 122

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

Problem Set 5 | Q 5 | Page 122

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

Problem Set 5 | Q 6.1 | Page 122

Find the distances between the following point.
A(a, 0), B(0, a)

Problem Set 5 | Q 6.2 | Page 122

Find the distances between the following point.

P(–6, –3), Q(–1, 9)

Problem Set 5 | Q 6.3 | Page 122

Find the distances between the following point.

R(–3aa), S(a, –2a)

Problem Set 5 | Q 7 | Page 122

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

Problem Set 5 | Q 8.1 | Page 123

In the following example, can the segment joining the given point form a triangle? If a triangle is formed, state the type of the triangle considering the side of the triangle.
L(6, 4), M(–5, –3), N(–6, 8)

Problem Set 5 | Q 8.2 | Page 123

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)

Problem Set 5 | Q 8.3 | Page 123

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.

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

Problem Set 5 | Q 9 | Page 123

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

Problem Set 5 | Q 10 | Page 123

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).

Problem Set 5 | Q 11 | Page 123

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

Problem Set 5 | Q 12 | Page 123

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

Problem Set 5 | Q 13 | Page 123

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

Problem Set 5 | Q 14 | Page 123

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.

Problem Set 5 | Q 15 | Page 123

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

Problem Set 5 | Q 16 | Page 123

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

Problem Set 5 | Q 17 | Page 123

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

Problem Set 5 | Q 18 | Page 123

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

Problem Set 5 | Q 19 | Page 123

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.

Problem Set 5 | Q 20 | Page 123

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

Problem Set 5 | Q 21 | Page 123

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).

Problem Set 5 | Q 22 | Page 123

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

## Chapter 5: Co-ordinate Geometry

Practice Set 5.1Practice Set 5.2Practice Set 5.3Problem Set 5 ## Balbharati solutions for Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board chapter 5 - Co-ordinate Geometry

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Concepts covered in Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board chapter 5 Co-ordinate Geometry are Centroid Formula, Co-ordinates of the Midpoint of a Segment, Section Formula, Distance Formula, Division of a Line Segment, 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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