# 10th Maths Book Back Coordinate Geometry Ex 5.3

## Samacheer Kalvi 10th Maths Book Back Solution:

Tamil Nadu 10th Maths Book Back Answers Unit 5 – Coordinate Geometry Ex 5.3 are provided on this page. Samacheer Kalvi Maths Book Back Solutions/ Guide available for all Units. TN Samacheer Kalvi 10th Maths Book consists of 8 Units and each unit book back solutions given below topics wise with Questions and Answers. The complete Samacheer Kalvi Books Back Answers/Solutions are available on our site.

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### 10th Maths Book Back Answers/Solutions:

TN Samacheer Kalvi 10th Maths Chapter 5 Book Back Exercise given below. The 10th Maths Book Back Solutions Guide is uploaded below:

### Exercise 5.3 Coordinate Geometry

1. Find the equation of a straight line passing through the mid-point of a line segment joining the points(1, -5) (4, 2) and parallel to
(i) X-axis
(ii) Y-axis
Solution:

2.The equation of a straight line is 2(x – y) + 5 = 0. Find its slope, inclination and intercept on the Y axis.
Solution:
2(x – y) + 5 = 0
⇒ 2x – 2y + 5 =
⇒ 2y = 2x + 5

3. Find the equation of a line whose inclination is 30° and make an intercept – 3 on the Y-axis.
Solution:
θ = 30°

4.Find the slope and y intercept of 3–√x + (1 – 3–√)y = 3.
Solution:

5.Find the value of ‘a’, if the line through (-2, 3) and (8, 5) is perpendicular to y = ax = + 2
Solution:

6. The hill in the form of a right triangle has its foot at (19, 3)The inclination of the hill to the ground is 45°. Find the equation of the hill joining the foot and top.
Solution:
θ = 45°
Coordinate of foot of hill = (19, 3) let equation of line be y = mx + c
m = tan θ = tan 45° = 1
⇒ y = x + c
Substituting y = 3 & x = 19, 3 = 19 + c ⇒ c = -16

7.Find the equation of a line through the given pair of points

(ii) (2, 3) and (-7, -1)
Solution:
(i) Equation of the line in two point form is

⇒ 9y – 27 = 4x – 8
⇒ 4x – 9y – 8 + 27 = 0
⇒ 4x – 9y + 19 = 0

8. A cat is located at the point(-6, -4) in XY plane. A bottle of milk is kept at (5, 11). The cat wishes to consume the milk traveling through the shortest possible distance. Find the equation of the path it needs to take its milk.
Solution:
A = (x1, y1) = (-6, -4)
B = (x2, y2) = (5, 11)

Shortest path between A and B is a line joining A and B.

9. Find the equation of the median and altitude of ∆ABC through A where the vertices are A(6, 2) B(-5, -1), and C(1, 9)
Solution:

10.Find the equation of a straight line which -5 has slope −54 and passing through the point (-1, 2).
Solution:

11.You are downloading a song. The percent y (in decimal form) of mega bytes remaining to get downloaded in x seconds is given by y = -0.1x + 1.
(i) graph the equation.
(ii) find the total MB of the song.
(iii) after how many seconds will 75% of the song gets downloaded?
Solution:
(i) y = -0.1x + 1
when x = 0 ⇒ y = 1
when y = 0 ⇒ y = 10

(ii) Total MB of song can be obtained when time = 0
∴ x = 0
⇒ y = 1 MB
⇒ remaining % = 25% ⇒ y = 0.25
0.25 = -0. 1x + 1
⇒ 0.1x = 0.75
⇒ 7.5 seconds.

(iv) song will downloaded completely when , remaining % = 0 ⇒ y = 0
⇒ 0 = -0.1x + 1
⇒ x = 10
∴ 10 seconds

12.Find the equation of a line whose intercepts on the x and y axes are given below.
(i) 4, -6
(ii) −534
Solution:

13.Find the intercepts made by the following lines on the coordinate axes,
(i) 3x – 2y – 6 = 0
(ii) 4x + 3y + 12 = 0
Solution:
(i) The given equation is
3x – 2y – 6 = 0
3x – 2y = 6
Divided by 6
3×6 – 2y6 = 66
x2 – y3 = 1 ⇒ x2 + y−3 = 1
(Comparing with xa + yb = 1)
∴ x intercept = 2; y intercept = -3

(ii) The given equation is
4x + 3y + 12 = 0
4x + 3y = -12
Divided by -12
4x−12 + 3y−12 = −12−12
x−3 + y−4 = 1
(Comparing with xa + yb = 1)
∴ x intercept = -3; y intercept = -4

14. Find the equation of a straight line
(i) passing through (1, -4) and has intercepts which are in the ratio 2 : 5
(ii) passing through (-8, 4) and making equal intercepts on the coordinate axes
Solution:
(i) ratio of intercept = 2 : 5