**KSEEB SSLC Solutions for Class 10 Maths – Coordinate Geometry (English Medium)**

**Exercise 13.1:**

**Question I:**

Locate the following points of a graph sheet.

- P (4, -3)
- R (-1, -1)
- I (0, -5)
- X(-5, -2)
- Y (3, 2)
- Z (4, 0)
- E (0, 6)
- F(-2, 5)

**Solution :**

**Question II:**

In which quadrants do these points lie?

i. (4, -6)

ii. (3, 1)

iii. (-10, -2)

iv. (-5, -2)

v. (-5, -1)

vi. (5, -7)

vii. (9, 9)

viii. (-2, 7)

**Solution :**

i. The point (4, -6) has positive x-coordinate (abscissa) and negative y-coordinate (ordinate). The point (4, -6) lies in IV^{th} quadrant.

ii. The point (3, 1) has positive x-coordinate (abscissa) and positive y-coordinate (ordinate). The point (3, 1) lies in I^{st} quadrant.

iii. The point (-10, -2) has negative x-coordinate (abscissa) and negative y-coordinate (ordinate). The point (-10, -2) lies in III^{rd} quadrant.

iv. The point (-5, -2) has negative x-coordinate (abscissa) and negative y-coordinate (ordinate). The point (-5, -2) lies in III^{rd} quadrant.

v. The point (-5, -1) has negative x-coordinate (abscissa) and negative y-coordinate (ordinate). The point (-5, -1) lies in III^{rd} quadrant.

vi. The point (5, -7) has positive x-coordinate (abscissa) and negative y-coordinate (ordinate). The point (5, -7) lies in IV^{th} quadrant.

vii. The point (9, 9) has positive x-coordinate (abscissa) and positive y-coordinate (ordinate). The point (9, 9) lies in I^{st} quadrant.

viii. The point (-2, 7) has negative x-coordinate (abscissa) and positive y-coordinate (ordinate). The point (-2, 7) lies in II^{nd} quadrant.

**Question III:**

Plot the points on a Cartesian plane whose

- Ordinate is 4, abscissa is 0
- Ordinate is -3, abscissa is -1
- Ordinate is 5, abscissa is 4
- Ordinate is -1, abscissa is 7

**Solution :**

- Ordinate is 4, abscissa is 0 = (0, 4)
- Ordinate is -3, abscissa is -1 = (-1, -3)
- Ordinate is 5, abscissa is 4 = (4, 5)
- Ordinate is -1, abscissa is 7= (7, -1)

**Exercise 13.2:**

**Question 1:**

Find the slope of the line whose inclination is

i. 90°

ii. 45°

iii. 30°

iv. 0°

**Solution :**

**Question 2:**

Find the angles of inclination of straight lines whose slopes are

**Solution :**

**Question 3:**

Find the slope of the line joining the points

**Solution :**

**Question 4:**

Find whether the lines drawn through the two pairs of points are parallel or perpendicular

i. (5,2), (0,5) and (0,0), (-5,3)

ii. (3,3), (4,6) and (4,1), (6,7)

iii. (4,7), (3,5) and (-1,7), (1,6)

iv. (-1,-2),(1,6) and (-1,1), (-2,-3)

**Solution :**

**Question 5:**

Find the slope of the line perpendicular to the line joining the points

i. (1, 7) and (-4, 3)

ii. (2, -3) and (1, 4)

**Solution :**

**Question 6:**

Find the slope of the line parallel to the line joining the points

i. (-4, 3) and (2, 5)

ii. (1, -5) and (7, 1)

**Solution :**

**Question 7:**

A line passing through the points (2,7) and (3,6) is parallel to the line joining (9, a) and (11, 3). Find the value of a.

**Solution :**

**Question 8:**

A line passing through the points (1, 0) and (4, 3) is perpendicular to the line joining (-2, -1) and (m, 0). Find the value of m.

**Solution :**

**Exercise 13.3:**

**Question 1:**

Find the equation of the line whose angle of inclination and y- intercept are given.

i. θ = 60° , y – intercept is – 2

ii. θ = 45° , y – intercept is 3

**Solution :**

**Question 2:**

Find the equation of the line whose slops and y-intercept are given.

i. Slope = 2, y- intercept = -4

iii. Slope = -2, y-intercept = 3

**Solution :**

**Question 3:**

Find the slope and y-intercept of the lines

i. 2x + 3y = 4

ii. 3x = y

iii. x – y + 5 = 0

iv. 3x – 4y = 5

**Solution :**

**Question 4:**

Is the line x = 2y parallel to 2x – 4y + 7 = 0 [** Hint **: Parallel lines have same slopes]

**Solution :**

**Question 5:**

Show that the line 3x + 4y + 7 = 0 and 28x – 21y + 50=0 are perpendicular to each other. [Hint : For perpendicular lines, m_{1}m_{2}=-1

**Solution :**

**Exercise 13.4:**

**Question 1:**

Find the distance between the following pairs of pointsi. (8, 3) and (8, -7)

ii. (1, -3) and (-4, 7)

iii. (-4, 5) and (-12, 3)

iv. (6, 5) and (4, 4)

v. (2, 0) and (0, 3)

vi. (2, 8) and (6, 8)

vii.(a, b) and (c, b)

viii. (cosθ, -sinθ) and (sinθ, -cosθ)

**Solution :**

**Question 2:**

Find the distance between the origin and the point

i. (-6, 8)

ii. (5, 12)

iii. (-8, 15)

**Solution :**

**Question 3(i):**

The distance between the points (3,1) and (0,x) is 5 units. Find x.

**Solution :**

**Question 3(ii):**

A point P (2,-1) is equidistant from the points (a, 7) and (-3, a). Find ‘a’.

**Solution :**

**Question 3(iii):**

Find a point on y-axis which is equidistant from the points (5,2) and (-4,3).

**Solution :**

**Question 4:**

Find the perimeter of the triangle whose vertices have the following coordinates

i. (-2, 1), (4, 6),(6, -3)

ii. (3, 10), (5, 2), (14, 12)

**Solution :**

**Question 5:**

Prove that the points A(1, -3), B(-3, 0) and C(4, 1) are the vertices of a right isosceles triangle.

**Solution :**

**Question 6:**

Find the radius of circle whose centre is (-5,4) and which passes through the point (-7,1).

**Solution :**

**Question 7:**

Prove that each of the set of coordinates are the vertices of parallelogram.

- (-5, -3), (1, -11), (7, -6), (1, 2)
- (4, 0), (-2, -3), (3, 2), (-3, -1)

**Solution :**

**Question 8:**

The coordinates of vertices of triangles are given. Identify the types of triangles.

i. (2,1) (10,1) (6,9)

ii. (1,6) (3,2) (10,8)

iii. (3,5) (-1,1) (6,2)

iv. (3,-3) (3,5) (11,-3)

**Solution :**

**Exercise 13.5:**

**Question 1:**

In what ratio does the point (-2,3) divide the line segment joining the points (-3,5) and (4,-9) ?

**Solution :**

**Question 2:**

In the point C(1,1) divides the line segment joining A(-2,7) and B in the ratio 3:2, Find the coordinates of B.

**Solution :**

**Question 3:**

Find the ratio in which the point (-1,k) divides the line joining the points (-3,10) and (6,-8).

**Solution :**

**Question 4:**

Find the coordinates of the midpoint of the line joining the points (-3,10) and (6,-8)

**Solution :**

**Question 5:**

Three consecutive vertices of a parallelogram are

A (1, 2), B (2, 3) and C (8, 5). Find the fourth vertex. (Hint : diagonals of a parallelogram bisect each other)

**Solution :**