5.7.3 The Straight Line, SPM Paper 2


Question 7:


The diagram above shows a parallelogram on a Cartesian plane. MP and NO are parallel to the y-axis. Given that the distance of MZ is 4 units. Find
(a) the value of p and q.
(b) the equation of the straight line MN.

Solution:
(a) Line NO is parallel to y-axis, p=2 MP= 3 2 + 4 2   = 9+16   = 25   =5 NO=MP=5 units q=75=2


(b) Point O=( 2,2 ) Gradient PO= 20 20 =1 Gradient MN=gradient PO=1 y 1 =m x 1 +c 7=1( 2 )+c c=5 Equation of line MN is y=x+5


Question 8:


The diagram above shows that two straight line intersect at point (0 , -2). Find
(a) the value of b
(b) the x-intercept of the straight line XY if the gradient of XY is equal to 2.
(c) the equation of XY.

Solution:
(a)
Value of b
= 2 units + 3 units
= 5 units
= –5

(b) Given m=2,c=2 For x-intercept, y=0 0=2x+( 2 ) 0=2x2 2x=2 x=1 Therefore x intercept of XY=1.

(c) Substitute m=2 and (0,2) into y=mx+c y=2x+( 2 ) y=2x2 Therefore equation of XY: y=2x2



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 PQ x-coordinate of P=0 For y-coordinate of P, y+0 2 =3 y=6 Coordinates of P=( 0,6 ).

(b) 0+4 2 =m 2m=4 m=2 Gradient of PR = 60 0( 4 ) = 6 4 = 3 2 At point N( n,4 ) using  y 1 =m x 1 +c 4= 3 2 n+6 8=3n+12 3n=4 n= 4 3

Leave a Reply

Your email address will not be published. Required fields are marked *