2024-2025
Form 4 Summer Quiz 01 (25 mins)
Equation of straight line
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Part A - MC (16 marks @2 marks)
Circle the answer.
1.
Given a straight line 2 x + 3 y + k = 0 . If the y-intercept is 4, then the x-intercept is
A.
−12 .
B.
−6 .
C.
6.
D. 12 .
2.
If the straight lines 2 x − 3 y + 1 = 0 and kx + y + 1 = 0 do not intersect with each other, then k =
A.
2
− .
3
B.
3
− .
2
C.
2
.
3
D.
3
.
2
1
3.
The x-intercept and the y-intercept of a straight line L are –4 and 6 respectively. If L1 passes through
the point (1, –2) and is parallel to L, the equation of L1 is
A. 3 x − 2 y − 7 = 0 .
B. 3 x − 2 y − 5 = 0 .
C. 3 x + 2 y + 1 = 0 .
D. 3 x + 2 y + 5 = 0 .
4.
The straight line L1 is perpendicular to the straight line L2 : 3x − 5 y + 10 = 0 and they intersect at
the y-axis. Find the equation of L1 .
A.
5 x − 3 y − 10 = 0
B.
5x + 3 y − 6 = 0
C.
3x − 5 y + 6 = 0
D.
3x + 5 y + 10 = 0
5.
If a  0 , which of the following shows the graph of the straight line ax + 3 y − 5 = 0 ?
A.
B.
C.
D.
2
6.
In the figure, the equation of straight line L1 and L2 are 4 x + by + c = 0 and kx + y + m = 0
respectively. Which of the following are true?
I.
bc
II. ck − 4m = 0
III. bk  4
A.
I and II only
B.
I and III only
C.
II and III only
D.
I, II and III
7.
It is given that A (1,5 ) and B ( 3, 7 ) . P is a point on the straight line 2 x − 3 y − 1 = 0 such that
PA = PB . Find the coordinate of P .
A.
( −4, −3)
B.
( 2,1)
C.
( 7, 3 )
D.
( 5, 3 )
8.
In the figure, ABCD is a parallelogram. Find the coordinates of D.
A.
( 2, 3 )
B.
( 3, 2 )
C.
( 4, 4 )
D.
( 5, 3 )
3
Part B - Short Questions (16 marks)
1.
Figure 1 shows the straight lines L . Given that A(5, 0) lies on x-axis while B(–2, 2) and C(8, 6) lie
on L . L cuts the x-axis at D.
(a) Find the equation of L .
(b) If AP is the shortest distance from A to L, find the coordinates of P.
(c) Find the ratio of the area of ΔADP to the area of ΔADB .
(8 marks)
4
5
2.
In the figure , ABC is a triangle and BC is a line parallel to x-axis. It is given that AC = DC and L
passes through E and C such that CE ⊥ AB.
(a) (i) Find the equation of AB.
(ii) Find the equation of L.
(b) It is further given that the coordinates of C are (13,𝑘), find the value of 𝑘. Hence, find the area of
ΔBCD.
(8 marks)
6
The end of the quiz
7