5.7 SPM Practice (Long Questions 5)

Question 9:


The diagram above shows that the straight line PMQ intersects with PNR at N. Given that OQ = OR and M is the midpoint of PQ. Find
(a) the coordinate of P
(b) the value of m and n.

Solution:
(a)Given M is midpoint of PQx-coordinate of P=0For y-coordinate of P,y+02=3y=6Coordinates of P=(0,6).

(b)0+42=m2m=4m=2Gradient of PR=600(4)=64=32At point N(n,4)using y1=mx1+c4=32n+68=3n+123n=4n=43



Question 10 (5 marks):
Diagram 6 shows two parallel straight lines, POQ and RMS drawn on a Cartesian plane.

Diagram 6

Find
(a) the equation of the straight line RMS,
(b) the x-intercept of the straight line MN.


Solution:
(a)
mRMS=mPOQ       =1020       =12At point (4, 6)y1=mx1+c6=12(4)+c6=2+cc=8The equation of straight line RMS isy=12x+8


(b)
When y=0,12x+8=012x=8x=16x-intercept of straight line MN is 16.