Mathematics Grade
JUNE TEST 2021
QUESTION A(1, 6), K(3, 0), C(12, 3) and D(x, y) are the vertices of a quadrilateral ABCD with AD / BC. E is the midpoint of BC. The angle of inclination of the straight line BC is 45° as shown in the diagram.
C(2, J)
1.1 Calculate the coordinates of E.
1.2 Determine the gradient of the line BC.
1.3 Calculate the magnitude of θ.
1.4 Prove that ∠ABC = 90°.
1.5 Determine the coordinates of vertex D given that x = 6.
1.6 Is AB parallel to CD? Motivate your answer by using analytical method.
1.7 What type of quadrilateral is ABCD? Give two reasons for your answer.
1.8 A straight line passing through vertex A and making an angle of 45° with side AD. Determine the equation of this straight line. [24]