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RD Chapter 7 Introduction to Euclid s Geometry Ex 7.4 Solutions

Question - 1 : -
Give the geometric representations of the following equations.
(a) on the number line
(b) on the cartesian plane.
(i) x – 2
(ii) y + 3 = 0
(iii) y = 3
(iv) 2x + 9 = 0
(v) 3x – 5 = 0

Answer - 1 : -

(i) x = 2
(i) on the number line
 
(ii) x = 2 is a line parallel to 7-axis at a distance of 2 units to right of y-axis.
(ii) y = -3 is a line parallel to x-axis at a distance of 3 units below x-axis.
 
(iii) y = 3
(i) y = 3
(ii) y = 3 is a line parallel to x-axis at a distance of 3 units above x-axis.
x = -4.5 is a line parallel to 7-axis at a distance of 4.5 units to left of y-axis.
(ii) x =   is a line parallel to y-axis at a  distance of   unit to right side of y-axis.

Question - 2 : -
Give the geometrical representation of 2x + 13 = 0 as an equation in
(i) One variable
(ii) Two variables

Answer - 2 : -

(i) In one variable,
2x + 13 = 0
⇒ 2x = – 13
⇒ x =  
is a line parallel to y-axis at a distance of -6 12 units on the left side of y-axis.

Question - 3 : -
Solve the equation 3x + 2 = x -8, and represent on
(i) the number line
(ii) the Cartesian plane.

Answer - 3 : -

3x + 2 = x – 8
⇒  3x – x = -8 – 2
⇒  2x = -10
⇒  x = −10/2 = -5
(i) on the number line s = -5
 
(ii) x = -5 is a line parallel to  y-axis at a distance of 5 knot’s left of y-axis.

Question - 4 : -
Write the equal of the line that is parallel to x-axis and passing through the points.
(i) (0, 3)                     
(ii)  (0, -4)
(iii) (2, -5)                     
(iv)    (3, 4)

Answer - 4 : -

∵  A line parallel to x-axis will be of the type y = a
∴ (i) y = 3
(ii) y = -4
(iii) y = -5 and y = 4 are equations of the lines parallel to x-axis

Question - 5 : -
Write the equation of the line that is parallel to y-axis and passing through the points.
(i) (4, 0)                      
(ii) (-2, 0)
(iii) (3, 5)                    
(iv) (-4, -3)

Answer - 5 : -

∵  A line parallel to y-axis will be of the type x = a
∴  (i) x = 4, (ii)  x = -2, x = 3 and x = -4 are the equations of the lines parallel to y-axis.

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