QUESTION 1
The diagram below shows ∆ABC, with vertices 𝐴(6; 8), 𝐵(− 4; − 2) and 𝐶(4; − 6).
D is the midpoint of BC. Study the diagram and answer the questions that follow.
1.1
Calculate the length of AB.
(2)
1.2
Calculate the length of BC.
(2)
1.3
Determine the coordinates of D, the midpoint of BC.
(2)
1.4
Prove that AD is the height of ∆ABC.
(5)
1.5
Prove that ∆ABC is isosceles.
(3)
[14]
QUESTION 2
The diagram below shows circle O. LMNP is a quadrilateral. MN produces to Q.
^
^
𝑀 = 47° and 𝑁𝑂𝑃 = 54°.
Determine, with reasons, the size of:
^
2.1
𝑀𝑁𝑂
2.2
𝑀𝑂𝑁
2.3
𝐿
2.4
𝑀𝑁𝑃
2.5
𝑃𝑁𝑄
^
^
(4)
(3)
(3)
^
^
(3)
(3)
[16]
QUESTION 3
The diagram below shows ∆PQR, with vertices 𝑃(2; 7), 𝑄(− 4; − 2) and 𝑅(4; 0).
T is the 𝑥-intercept of PQ and 𝑈(0; 1) is the 𝑦-intercept of QR. P, R and S are
collinear.
3.1
Determine the gradient of PS.
3.2
Determine the size of:
(2)
3.2.1 α
(2)
3.2.2 β
(3)
3.2.3 θ
(3)
^
3.3
3.2.4 𝑄𝑅𝑆.
(5)
Determine the equation of the line passing through U and parallel to PS.
(5)
[20]
TOTAL: 50