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 S R = 6 3 = 2

(b)
Gradient of Q R = 8 6 5 0 = 2 5  
Substitute 2 5 and R (5, 8) into y = mx + c
8 =  2 5 (5) + 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)
5 x + 7 y + 35 = 0 7 y = 5 x 35 y = 5 7 x 5 The gradient of the straight line R S = 5 7 .
(b)
At x-intercept, y = 0 0 = 5 7 x 5 5 7 x = 5 x = 7 x-intercept of the straight line R S = 7.
(c)
Point R = ( 7 , 0 ) and point S = ( 0 , 5 ) Distance of R S = ( 7 0 ) 2 + ( 0 ( 5 ) ) 2 Distance of R S = 49 + 25 Distance of R S = 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 A O = Gradient of O B 0 ( 4 ) 0 ( 3 ) = h 0 6 0 4 3 = h 6 h = 8
(c)
Gradient of B C = 8 0 6 ( 6 ) = 8 12 = 2 3 At point C ( 6 , 0 ) , 0 = 2 3 ( 6 ) + c c = 4 The equation of B C is, y = 2 3 x + 4

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