Introduction to Euclid’s Geometry RD Sharma Class 9 Solutions
RD Sharma Solutions Class 9 Chapter 7 Introduction to Euclid’s Geometry Ex 7.1
Question 1.
Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case:
(i) -2x + 3y = 12
(ii) x-\(\frac { y }{ 2 }\) -5 = 0
(iii) 2x + 3y = 9.35
(iv) 3x = -7y
(v) 2x + 3 = 0
(vi) y – 5 = 0
(vii) 4 = 3x
(viii) y = \(\frac { x }{ 2 }\)
Solution:
(i) -2x + 3y = 12
⇒ -2x + 3y – 12 = 0
Here a -2, b = 3, c = – 12
(ii) x – \(\frac { y }{ 2 }\) -5 = 0
Here a = 1, b =\(\frac { 1 }{ 2 }\) ,c = -5
(iii) 2x + 3y = 9.35
⇒ 2x + 3y – 9.35 = 0
Here a = 2, b = 3, c = – 9.35
(iv) 3x = -7y
⇒ 3x + 7y + 0 = 0
Here a = 3, b = 7,c = 0
(v) 2x + 3 = 0
⇒ 2x + 0y + 3 = 0
Here a = 2, b = 0, c = 3
(vi) y-5 = 0 ⇒ ox+y-5 = 0
Here a = 0, b = 1, c = -5
(vii) 4 = 3x
⇒ 3x – 4 = 0
⇒ 3x + 0y – 4 = 0
Here a = 3, b = 0, c = -4
(Viii) y= \(\frac { x }{ 2 }\)
⇒ \(\frac { x }{ 2 }\) – y+ 0 = 0
⇒ x-2y + 0 = 0
Here a = 1, y = -2, c = 0
Question 2.
Write each of the following as an equation in two variables.
(i) 2x = -3
(ii) y = 3
(iii) 5x = \(\frac { 7 }{ 2 }\)
(iv) y =\(\frac { 3 }{ 2 }\)x
Solution:
(i) 2x = -3⇒ 2x + 3 = 0
⇒ 2x + 0y + 3 = 0
(ii) y= 3 ⇒ y-3=0
⇒ 0x+ y-3 = 0
(iii) 5x =\(\frac { 7 }{ 2 }\) ⇒ 10x = 7
⇒ 10x + 0y – 7 = 0
(iv) y=\(\frac { 3 }{ 2 }\)x⇒2y = 3x
⇒ 3x – 2y + 0 = 0
Question 3.
The cost of ball pen is ₹5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.
Solution:
Let cost of a fountain pen = ₹x
and cost of ball pen = ₹y
∴ According to the condition,
y = \(\frac { x }{ 2 }\) -5
⇒ 2y = x – 10
⇒ x – 2y – 10 = 0
Introduction to Euclid’s Geometry RD Sharma Class 9 Solutions
2 (i)
Infinitely many
2 (ii)
one
3 (i)
one
3 (ii)
PQ,QR,PR
RD Sharma Class 9 Solutions