Coordinate Geometry Short Questions (Question 3, 4 & 5)


Question 3:
The equation of the straight lines CD and EF are 5x + y – 4 = 0 and x 7 y h =1 . If CD and EF are parallel, find the value of h.

Solution:
                                 Two parallel lines have same gradient.
                                 5x + y – 4 = 0  
                                 y = –5x + 4, mCD = –5    

                                 For the straight line EF,
x 7 y h =1 m EF =( y-intercept x-intercept )=( h 7 )= h 7 m CD = m EF 5= h 7 h=35



Question 4:
The straight line x 5 + y p =1 has a y-intercept of 3 and is parallel to the straight line y + qx = 0. Determine the value of p and of q.

Solution:
Given y-intercept of the straight line  x 5 + y p =1 is 3, p=3 Gradient of the straight line =  3 5 For another straight line y+qx=0, y=qx As two parallel lines have same gradient, q= 3 5 q= 3 5


Question 5:
The equations of two straight lines   y 7 + x 4 =1 and 7y = 4x + 21. Determine whether the lines are perpendicular to each other.

Solution:
For the straight line  y 7 + x 4 =1, gradient = 7 4 For the straight line 7y=4x+21, y= 4 7 x+3, gradient = 4 7 7 4 × 4 7 =1
Hence, the two straight lines are perpendicular to each other.