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

## Chapter 5: Co-ordinate Geometry

#### Chapter 5: Co-ordinate Geometry solutions [Pages 107 - 108]

Q 1.1 | Page 107

Find the distance between the following pair of point.

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

Q 1.2 | Page 107

Find the distance between the following pair of point.

P(–5, 7), Q(–1, 3)

Q 1.3 | Page 107

Find the distance between the following pair of point.

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

Q 1.4 | Page 107

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

L(5, –8), M(–7, –3)

Q 1.5 | Page 107

Find the distance between the following pair of point.

T(–3, 6), R(9, –10)

Q 1.6 | Page 107

Find the distance between the following pair of point.

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

Q 2.1 | Page 107

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

Q 2.2 | Page 107

Determine whether the point is collinear.

L(–2, 3), M(1, –3), N(5, 4)

Q 2.3 | Page 107

Determine whether the point is collinear.

R(0, 3), D(2, 1), S(3, –1)

Q 2.4 | Page 107

Determine whether the point is collinear.

P(–2, 3), Q(1, 2), R(4, 1)

Q 3 | Page 107

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

Q 4 | Page 107

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

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.

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.

Q 7 | Page 108

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

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.

#### Chapter 5: Co-ordinate Geometry solutions [Pages 115 - 116]

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.

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

Q 2.2 | Page 115

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

P(–2, –5), Q(4, 3), = 3 : 4

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

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).

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.

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 ?

Q 6 | Page 115

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

Q 7.1 | Page 115

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

(–7, 6), (2, –2), (8, 5)

Q 7.2 | Page 115

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

(3, –5), (4, 3), (11, –4)

Q 7.3 | Page 115

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

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

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.

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.

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).

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.

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.

#### Chapter 5: Co-ordinate Geometry solutions [Pages 121 - 122]

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°

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°

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°

Q 2.1 | Page 121

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

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

Q 2.2 | Page 121

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

P (–3, 1) , Q (5, –2)

Q 2.3 | Page 121

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

C (5, –2) , ∆ (7, 3)

Q 2.4 | Page 121

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

L (–2, –3) , M (–6, –8)

Q 2.5 | Page 121

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

E(–4, –2) , F (6, 3)

Q 2.6 | Page 121

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

T (0, –3) , S (0, 4)

Q 3.1 | Page 121

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

Q 3.2 | Page 121

Determine whether the following point is collinear.

D(–2, –3), E(1, 0), F(2, 1)

Q 3.3 | Page 121

Determine whether the following point is collinear.

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

Q 3.4 | Page 121

Determine whether the following point is collinear.

P(2, –5), Q(1, –3), R(–2, 3)

Q 3.5 | Page 121

Determine whether the following point is collinear.

R(1, –4), S(–2, 2), T(–3, 4)

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)

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.

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.

Q 6 | Page 122

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

Q 7 | Page 122

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

Q 8 | Page 122

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

#### Chapter 5: Co-ordinate Geometry solutions [Pages 122 - 123]

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 ........ .
(A) (3,1)
(B) (5,3)
(C) (3,0)
(D) (1,–3)

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.
(A) (–2,0)
(B) (0,2)
(C) (2,3)
(D) (2,0)

Q 1.3 | Page 122

Fill in the blank using correct alternative.

Distance of point (–3,4) from the origin is ...... .
(A) 7
(B) 1
(C) 5
(D) –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 .......... .

(A)$\frac{1}{2}$

(B) $\frac{\sqrt{3}}{2}$

(C) $\frac{1}{\sqrt{3}}$

(D) $\sqrt{3}$

Q 2.1 | Page 122

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

Q 2.2 | Page 122

Determine whether the given point is collinear.

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

Q 2.3 | Page 122

Determine whether the given point is collinear.

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

Q 3 | Page 122

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

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.

Q 5 | Page 122

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

Q 6.1 | Page 122

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

Q 6.2 | Page 122

Find the distances between the following point.

P(–6, –3), Q(–1, 9)

Q 6.3 | Page 122

Find the distances between the following point.

R(–3aa), S(a, –2a)

Q 7 | Page 122

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

Q 8.1 | 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.
L(6,4) , M(–5,–3) , N(–6,8)

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)

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.

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

Q 9 | Page 123

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

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).

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.

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 .

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).

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.

Q 15 | Page 123

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

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.

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.

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.

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.

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).

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).

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).

## 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.

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

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.

Using Balbharati Class 10th Board Exam solutions Co-ordinate Geometry 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 Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board Class 10th Board Exam prefer Balbharati Textbook Solutions to score more in exam.

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