Page 17 - 1202 Question Bank Additional Mathematics Form 4

10. Diagram 10 shows a parallelogram ABCD.
A
B

M
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D L
N
C
Diagram 10
→
1 → →
→ →
→
NLM is a straight line and AL is perpendicular to DC. Given DL = DC, CB = 4CM, LA = 2x and DA = 8y.
~
~
4
(a) Express, in terms of x and y,
→
(i) DL,
→
(ii) LM.
→
→
→
(b) Given ND = ky and NL = hLM, find the value of h and k.
~
(c) If |x| = 3 units and |y| = 2.5 units, find
~ →
(i) |DC|, ~
(ii) the area of the parallelogram ABCD.
[10 marks]
11. A straight line with gradient of 4 passes through A(–2, 5) and intercepts the x-axis at B. Another straight line passes
through A and intersects the x-axis at C(2, 0).
(a) Find the equation of the line AB and AC. [2 marks]
(b) Calculate the area of the triangle ABC. [2 marks]
(c) Find the coordinates of D so that ABCD is a parallelogram. [3 marks]
(d) A point P(x, y) moves such that ∠APC is always 90°. Find the equation of locus of point P. [3 marks]

Section C
[20 marks]
Answer any two questions from this section.

12. Diagram 12 shows a pyramid with a equilateral base of side 8 cm.
V

Q

L
P
M
8 cm
N
Diagram 12
V is 5 cm vertically above P where P is the midpoint of LM. Given that ∠VNQ = ∠QNM, find
(a) the length of VN, [2 marks]
(b) ∠QNM, [3 marks]
(c) the length of QM, [2 marks]
(d) the area of the inclined plane, VNM. [3 marks]
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