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5.7 SPM Practice (Long Questions 3)

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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 AO= Gradient of OB 0−( −4 ) 0−( −3 ) = h−0 6−0 4 3 = h 6 h=8

(c)
Gradient of BC= 8−0 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