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## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.3

10th Maths Exercise 5.3 Samacheer Kalvi Question 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:

Exercise 5.3 Class 10 Samacheer Kalvi Question 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

Ex 5.3 Class 10 Samacheer Question 3.

Find the equation of a line whose inclination is 30° and making an intercept – 3 on the Y axis.

Solution:

θ = 30°

10th Samacheer Maths Exercise 5.3 Answers Question 4.

Find the slope and y intercept of \(\sqrt{3}\)x + (1 – \(\sqrt{3}\))y = 3.

Solution:

10th Maths Coordinate Geometry Exercise 5.3 Question 5.

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

Solution:

10th Maths Exercise 5.3 Question 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

Question 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

10th Standard Maths Exercise 5.3 Question 8.

A cat is located at the point(-6, -4) in xy plane. A bottle of milk is kept at (5, 11). The cat wish to consume the milk traveling through shortest possible distance. Find the equation of the path it needs to take its milk.

Solution:

A = (x_{1}, y_{1}) = (-6, -4)

B = (x_{2}, y_{2}) = (5, 11)

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

10th Maths 5.3 Question 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:

10th Samacheer Kalvi Maths Coordinate Geometry Question 10.

Find the equation of a straight line which -5 has slope \(\frac{-5}{4}\) and passing through the point (-1, 2).

Solution:

Ex 5.3 Class 10 Question 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?

(iv) after how many seconds the song will be downloaded completely?

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

(iii) time when 75% of song is downloaded

⇒ remaining % = 25% ⇒ y = 0.25

0.25 = -0. 1x + 1

⇒ 0.1x = 0.75

(iv) song will downloaded completely when , remaining % = 0 ⇒ y = 0

⇒ 0 = -0.1x + 1

⇒ x = 10

∴ 10 seconds

Exercise 5.3 Class 10 Question 12.

Find the equation of a line whose intercepts on the x and y axes are given below.

(i) 4, -6

(ii) \(-5 \frac{3}{4}\)

Solution:

5.3 Class 10 Question 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

\(\frac { 3x }{ 6 } \) – \(\frac { 2y }{ 6 } \) = \(\frac { 6 }{ 6 } \)

\(\frac { x }{ 2 } \) – \(\frac { y }{ 3 } \) = 1 ⇒ \(\frac { x }{ 2 } \) + \(\frac { y }{ -3 } \) = 1

(Comparing with \(\frac { x }{ a } \) + \(\frac { y }{ b } \) = 1)

∴ x intercept = 2; y intercept = -3

(ii) The given equation is

4x + 3y + 12 = 0

4x + 3y = -12

Divided by -12

\(\frac { 4x }{ -12 } \) + \(\frac { 3y }{ -12 } \) = \(\frac { -12 }{ -12 } \)

\(\frac { x }{ -3 } \) + \(\frac { y }{ -4 } \) = 1

(Comparing with \(\frac { x }{ a } \) + \(\frac { y }{ b } \) = 1)

∴ x intercept = -3; y intercept = -4

10th Maths Exercise 5.2 Samacheer Kalvi Question 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