Topical Revision Paper 9 Unit 9 Points Lines Shapes Students

Topical Revision Paper 9 Term 3 Unit 9: Points, Lines and Shapes Question 1: The vertices of a triangle ABC are A (5, 10), B (0, 0) and C (–6, 8). (i) Show that the triangle ABC is an isosceles triangle. [2] (ii) Calculate the area of triangle ABC. [2] (iii) Find the coordinates of the foot of perpendicular from A to BC. [1] (iv) Given that four points A, B, C and D form a rhombus, find the coordinates of the point D. [3] (v) Find the equation of AC. Hence or otherwise, find the coordinates of the foot of perpendicular from B to AC. [5] Answer: (ii) 50 units 2 (iii) (3, 4) (iv)  11, 2 (v) 8 44,55  Question 2 : The diagram below shows triangle ANC. Point B has coordinates (8,0) , Point C has coordinates (4,7) and Point D has coordinates ( 2,5) . The equation of the straight line DB is 2x y k and this line intersects the y-axis at A. Point N lies on the line DB such that CN is perpendicular to line DB. Point F is on the x-axis such that DF is parallel to the y-axis.

(i) Find the value of k, in the equation of straight line DB. [2] (ii) Find (a) the gradient of CN, [2] (b) the equation of CN. [1] (iii) Calculate the coordinates of N. [2] (iv) Is CN a perpendicular bisector of BD? Explain your answer. [1] (v) Calculate the area of triangle DFB. [3] (vi) Show clearly that the distance between D and B is 11.18 units, correct to 2 decimal places. [2] (vii) Find the perpendicular distance of F to BD. [2] Answer: (i) 8 (ii) (a) Gradient of CN = 2 (b) 21yx (iii) (2,3)N  (v) 25 units2 (vii) 4.47 x y D ( 2, 5) x + 2y = kN A O C (4, 7) B (8, 0) F

Question 3: Solutions to this question by accurate drawing will not be accepted. The diagram shows a rhombus ABCD with vertices A(10,k), B, C(–2,–2) and D in which the equation of line BC is given to be 8 14 0yx   and the equation of line BD is 2 3 16 0yx   . (i) Show that k = 6. [3] (ii) Find the coordinates of B and of D. [6] (iii) Find the area of the rhombus ABCD. [2] Answer: (ii) : (6, 1)B  : (2,5)D (iii) 52 units 2 Question 4: Solutions to this question by accurate drawing will not be accepted. (-5, -3) (6, 6) (-2, 3) o x y F E P C A B D x A (10, )k C ( 2, 2) B D y

The diagram shows a trapezium ABCD in which AB is parallel to DC and BC is a vertical line. The vertices of the trapezium are A(–2, 3), B(6, 6), C and D(–5, –3). The perpendicular from A to DC meets DC at the point P. (i) Find the coordinates of P and C. [6] The lines AB and DC cut the y-axis at E and F respectively. (ii) Find the area of the parallelogram BCFE. [2] Answer: (i) 29 20: , 1 73 73P  1: 6,1 8C   (ii) 29.25 units2