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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:
10th Maths Exercise 5.3 Samacheer Kalvi Chapter 5 Coordinate Geometry
Exercise 5.3 Class 10 Samacheer Kalvi Chapter 5 Coordinate Geometry

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 Chapter 5 Coordinate Geometry

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 Chapter 5 Coordinate Geometry

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 Exercise 5.3 Samacheer Kalvi Chapter 5 Coordinate Geometry

10th Maths 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 Coordinate Geometry Exercise 5.3 Samacheer Kalvi Chapter 5
10th Maths 5.3 Samacheer Kalvi Solutions Chapter 5 Coordinate Geometry

10th Maths Coordinate Geometry 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
10th Standard Maths Exercise 5.3 Samacheer Kalvi Chapter 5 Coordinate Geometry

10th Maths 5.3 Question 7.
Find the equation of a line through the given pair of points
10th Exercise 5.3 Samacheer Kalvi Chapter 5 Coordinate Geometry
(ii) (2, 3) and (-7, -1)
Solution:
(i) Equation of the line in two point form is
10th Maths 5.3 Solution Samacheer Kalvi Chapter 5 Coordinate Geometry
10th Samacheer Kalvi Maths Coordinate Geometry Chapter 5 Ex 5.3
⇒ 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 = (x1, y1) = (-6, -4)
B = (x2, y2) = (5, 11)
Shortest path between A and B is a line joining A and B.
10 Maths Exercise 5.3 Samacheer Kalvi Chapter 5 Coordinate Geometry

10th Exercise 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:
Maths Exercise 5.3 Samacheer Kalvi 10th Solutions Chapter 5 Coordinate Geometry
Ex 5.3 Class 10 Maths Solutions Samacheer Kalvi Chapter 5 Coordinate Geometry

10th Maths 5.3 Solution Question 10.
Find the equation of a straight line which -5 has slope \(\frac{-5}{4}\) and passing through the point (-1, 2).
Solution:
10th Maths Chapter 5 Exercise 5.3 Samacheer Kalvi Coordinate Geometry

10th Samacheer Kalvi Maths Coordinate Geometry 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
Exercise 5.3 Class 10 Samacheer Kalvi Chapter 5 Coordinate Geometry
(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
Ex 5.3 Class 10 Samacheer Kalvi Maths Solutions Chapter 5 Coordinate Geometry
(iv) song will downloaded completely when , remaining % = 0 ⇒ y = 0
⇒ 0 = -0.1x + 1
⇒ x = 10
∴ 10 seconds

10 Maths Exercise 5.3 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:
Samacheer Kalvi 10th Guide Maths Solutions Chapter 5 Coordinate Geometry Ex 5.3

Maths Exercise 5.3 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

Ex 5.3 Class 10 Maths Solutions 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
Samacher Kalvi.Guru 10th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.3

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