# NCERT solutions for Mathematics Exemplar Class 10 chapter 7 - Coordinate Geometry [Latest edition]

## Chapter 7: Coordinate Geometry

Exercise 7.1Exercise 7.2Exercise 7.3Exercise 7.4
Exercise 7.1 [Pages 78 - 80]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 7 Coordinate Geometry Exercise 7.1 [Pages 78 - 80]

#### Choose the correct alternative:

Exercise 7.1 | Q 1 | Page 78

The distance of the point P(2, 3) from the x-axis is ______.

• 2

• 3

• 1

• 5

Exercise 7.1 | Q 2 | Page 78

The distance between the points A(0, 6) and B(0, –2) is ______.

• 6

• 8

• 4

• 2

Exercise 7.1 | Q 3 | Page 78

The distance of the point P(–6, 8) from the origin is ______.

• 8

• 2sqrt(7)

• 10

• 6

Exercise 7.1 | Q 4 | Page 78

The distance between the points (0, 5) and (–5, 0) is ______.

• 5

• 5sqrt(2)

• 2sqrt(5)

• 10

Exercise 7.1 | Q 5 | Page 78

AOBC is a rectangle whose three vertices are vertices A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.

• 5

• 3

• sqrt(34)

• 4

Exercise 7.1 | Q 6 | Page 78

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.

• 5 units

• 12 units

• 11 units

• 7 + sqrt(5) units

Exercise 7.1 | Q 7 | Page 78

The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is ______.

• 14

• 28

• 8

• 6

Exercise 7.1 | Q 8 | Page 78

The points (–4, 0), (4, 0), (0, 3) are the vertices of a ______.

• Right triangle

• Isosceles triangle

• Equilateral triangle

• Scalene triangle

Exercise 7.1 | Q 9 | Page 79

The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the ______.

Exercise 7.1 | Q 10 | Page 79

The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is ______.

• (0, 0)

• (0, 2)

• (2, 0)

• (–2, 0)

Exercise 7.1 | Q 11 | Page 79

The fourth vertex D of a parallelogram ABCD whose three vertices are A(–2, 3), B(6, 7) and C(8, 3) is ______.

• (0, 1)

• (0, –1)

• (–1, 0)

• (1, 0)

Exercise 7.1 | Q 12 | Page 79

If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.

• AP = 1/3AB

• AP = PB

• PB = 1/3AB

• AP = 1/2AB

Exercise 7.1 | Q 13 | Page 79

If P(a/3, 4) is the mid-point of the line segment joining the points Q(– 6, 5) and R(– 2, 3), then the value of a is ______.

• – 4

• – 12

• 12

• – 6

Exercise 7.1 | Q 14 | Page 79

The perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis at ______.

• (0, 13)

• (0, –13)

• (0, 12)

• (13, 0)

Exercise 7.1 | Q 15 | Page 79

The coordinates of the point which is equidistant from the three vertices of the ∆AOB as shown in the figure is ______.

• (x, y)

• (y, x)

• x/2, y/2

• y/2, x/2

Exercise 7.1 | Q 16 | Page 79

A circle drawn with origin as the centre passes through (13/2, 0). The point which does not lie in the interior of the circle is ______.

• (-3)/4, 1

• 2, 7/3

• 5, (-1)/2

• (-6, 5/2)

Exercise 7.1 | Q 17 | Page 80

A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid-point of PQ, then the coordinates of P and Q are, respectively ______.

• (0, – 5) and (2, 0)

• (0, 10) and (– 4, 0)

• (0, 4) and (– 10, 0)

• (0, – 10) and (4, 0)

Exercise 7.1 | Q 18 | Page 80

The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is ______.

• (a + b + c) 2

• 0

• a + b + c

• abc

Exercise 7.1 | Q 19 | Page 80

If the distance between the points (4, p) and (1, 0) is 5, then the value of p is ______.

• 4 only

• ± 4

• – 4 only

• 0

Exercise 7.1 | Q 20 | Page 80

If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then ______.

• a = b

• a = 2b

• 2a = b

• a = –b

Exercise 7.2 [Pages 80 - 81]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 7 Coordinate Geometry Exercise 7.2 [Pages 80 - 81]

#### State whether the following statement is True or False:

Exercise 7.2 | Q 1 | Page 80

∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0) E(4, 0) and F(0, 4).

• True

• False

Exercise 7.2 | Q 2 | Page 81

Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).

• True

• False

Exercise 7.2 | Q 3 | Page 81

The points (0, 5), (0, –9) and (3, 6) are collinear.

• True

• False

Exercise 7.2 | Q 4 | Page 81

Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).

• True

• False

Exercise 7.2 | Q 5 | Page 81

Points A(3, 1), B(12, –2) and C(0, 2) cannot be the vertices of a triangle.

• True

• False

Exercise 7.2 | Q 6 | Page 81

Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.

• True

• False

Exercise 7.2 | Q 7 | Page 81

A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.

• True

• False

Exercise 7.2 | Q 8 | Page 81

The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).

• True

• False

Exercise 7.2 | Q 9 | Page 81

Point P(5, –3) is one of the two points of trisection of the line segment joining the points A(7, – 2) and B(1, – 5).

• True

• False

Exercise 7.2 | Q 10 | Page 81

Points A(–6, 10), B(–4, 6) and C(3, –8) are collinear such that AB = 2/9 AC.

• True

• False

Exercise 7.2 | Q 11 | Page 81

The point P (–2, 4) lies on a circle of radius 6 and centre C (3, 5).

• True

• False

Exercise 7.2 | Q 12 | Page 81

The points A(–1, –2), B (4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.

• True

• False

Exercise 7.3 [Pages 83 - 84]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 7 Coordinate Geometry Exercise 7.3 [Pages 83 - 84]

Exercise 7.3 | Q 1 | Page 83

Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).

Exercise 7.3 | Q 2 | Page 83

Find the points on the x-axis which are at a distance of 2sqrt(5) from the point (7, –4). How many such points are there?

Exercise 7.3 | Q 3 | Page 83

What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?

Exercise 7.3 | Q 4 | Page 83

Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.

Exercise 7.3 | Q 5 | Page 83

Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?

Exercise 7.3 | Q 6 | Page 84

Find the coordinates of the point Q on the x-axis which lies on the perpendicular bisector of the line segment joining the points A(–5, –2) and B(4, –2). Name the type of triangle formed by the points Q, A and B.

Exercise 7.3 | Q 7 | Page 84

Find the value of m if the points (5, 1), (–2, –3) and (8, 2m) are collinear.

Exercise 7.3 | Q 8 | Page 84

If the point A(2, – 4) is equidistant from P(3, 8) and Q (–10, y), find the values of y. Also find distance PQ.

Exercise 7.3 | Q 9 | Page 84

Find the area of the triangle whose vertices are (–8, 4), (–6, 6) and (–3, 9).

Exercise 7.3 | Q 10 | Page 84

In what ratio does the x-axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.

Exercise 7.3 | Q 11 | Page 84

Find the ratio in which the point P(3/4, 5/12) divides the line segment joining the points A(1/2, 3/2) and B(2, –5).

Exercise 7.3 | Q 12 | Page 84

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

Exercise 7.3 | Q 13 | Page 84

If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.

Exercise 7.3 | Q 14 | Page 84

The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, –9) and has diameter 10sqrt(2) units

Exercise 7.3 | Q 15 | Page 84

The line segment joining the points A(3, 2) and B(5,1) is divided at the point P in the ratio 1:2 and it lies on the line 3x – 18y + k = 0. Find the value of k.

Exercise 7.3 | Q 16 | Page 84

If D((-1)/2, 5/2), E(7, 3) and F(7/2, 7/2) are the midpoints of sides of ∆ABC, find the area of the ∆ABC.

Exercise 7.3 | Q 17 | Page 84

The points A(2, 9), B(a, 5) and C(5, 5) are the vertices of a triangle ABC right angled at B. Find the values of a and hence the area of ∆ABC.

Exercise 7.3 | Q 18 | Page 84

Find the coordinates of the point R on the line segment joining the points P(–1, 3) and Q(2, 5) such that PR = 3/5 PQ.

Exercise 7.3 | Q 19 | Page 84

Find the values of k if the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear.

Exercise 7.3 | Q 20 | Page 84

Find the ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1). Also find the coordinates of the point of division.

Exercise 7.4 [Pages 85 - 86]

### NCERT solutions for Mathematics Exemplar Class 10 Chapter 7 Coordinate Geometry Exercise 7.4 [Pages 85 - 86]

Exercise 7.4 | Q 1 | Page 85

If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

Exercise 7.4 | Q 2 | Page 85

A(6, 1), B(8, 2) and C(9, 4) are three vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of ∆ADE.

Exercise 7.4 | Q 3.(i) | Page 86

The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. The median from A meets BC at D. Find the coordinates of the point D.

Exercise 7.4 | Q 3.(ii) | Page 86

The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. Find the coordinates of the point P on AD such that AP : PD = 2 : 1

Exercise 7.4 | Q 3.(iii) | Page 86

The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC.  Find the coordinates of points Q and R on medians BE and CF, respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1

Exercise 7.4 | Q 3.(iv) | Page 86

The points A(x1, y1), B(x2, y2) and C(x3, y3) are the vertices of ∆ABC. What are the coordinates of the centroid of the triangle ABC?

Exercise 7.4 | Q 4 | Page 86

If the points A(1, –2), B(2, 3) C(a, 2) and D(– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.

Exercise 7.4 | Q 5 | Page 86

Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?

Exercise 7.4 | Q 6 | Page 86

Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.

## Chapter 7: Coordinate Geometry

Exercise 7.1Exercise 7.2Exercise 7.3Exercise 7.4

## NCERT solutions for Mathematics Exemplar Class 10 chapter 7 - Coordinate Geometry

NCERT solutions for Mathematics Exemplar Class 10 chapter 7 (Coordinate 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 CBSE Mathematics Exemplar Class 10 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 10 chapter 7 Coordinate Geometry are Section Formula, Graphs of Linear Equations, Distance Formula, Coordinate Geometry, Coordinate Geometry, Basic Geometric Constructions, Area of a Triangle.

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