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=6−00−(−4)=64=32At point N(n,4), using y1=mx1+c4=32n+68=3n+123n=−4n=−43

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=6−00−(−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 =1−0−2−0 =−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.
Diagram 6 shows two parallel straight lines, POQ and RMS drawn on a Cartesian plane.

Find
(a) the equation of the straight line RMS,
(b) the x-intercept of the straight line MN.
Solution:
(a)
mRMS=mPOQ =1−0−2−0 =−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.