The Straight Line Long questions (Question 4 - 6)


Question 4:

In the diagram above, PQRS is a parallelogram. Find
(a)  the gradient of SR,
(b) the equation of QR,
(c)  the x-intercept of QR.

Solution:
(a)
PQ is parallel to SR, gradient of PQ = gradient of SR.
Gradient of SR= 6 3 =2

(b)
Gradient of QR= 86 50 = 2 5 
Substitute m 2 5 and R (5, 8) into y = mx + c
8 =  2 5 (5) + c
c = 6

Therefore equation of QR y= 2 5 x+6

(c)
For x-intercept, y=0 0= 2 5 x+6 x=15
Therefore x-intercept of QR = –15.


Question 5:

In the diagram above, a straight line 5x +7y + 35 = 0 intersects with the x-axis and y-axis at R and S respectively. Determine
(a) the gradient of the straight line RS.
(b) the x-intercept of the straight line RS.
(c) the distance of RS.

Solution:
(a)
5x+7y+35=0 7y=5x35 y= 5 7 x5  The gradient of the straight line RS= 5 7 .
(b)
At x-intercept, y=0 0= 5 7 x5 5 7 x=5 x=7  x-intercept of the straight line RS=7.
(c)
Point R=( 7,0 ) and point S=( 0,5 ) Distance of RS= ( 70 ) 2 + ( 0( 5 ) ) 2 Distance of RS= 49+25 Distance of RS= 74  units


Question 6:

In the diagram above, O is the origin of the Cartesian plane, AOB is a straight line and OA = AC. Find
(a) the coordinates of C.
(b) the value of h.
(c) the equation of BC.

Solution:
(a)
x-coordinate of C = –3 × 2 = –6
Therefore coordinates of C = (–6, 0).

(b)
Gradient of AO= Gradient of OB 0( 4 ) 0( 3 ) = h0 60 4 3 = h 6 h=8
(c)
Gradient of BC= 80 6( 6 ) = 8 12 = 2 3 At point C( 6,0 ), 0= 2 3 ( 6 )+c c=4 The equation of BC is, y= 2 3 x+4