! ! ! ! "#!$%&'()*!+,-! ! ! ! !"#$%&'"()%*+,( 0.1 Distance between Two Points 0.2 Slope of a Straight Line 1 0.3 Parallel and Perpendicular Lines 2 1.1 Point of Division 如果係 1 : 1 1. M is the mid-point of the line segment joining A(1, 8) and B(7, 2). Find the coordinates of M. [(4, 5)] 2. Referring to the figure, N is the mid-point of CD. Find the coordinates of C. [(–19, –10)] 3 3. Given that the line segment joining A(4, 5) and M(7, 9) is produced to a point B and AM = MB, find the coordinates of B. 4. [(10, 13)] Q is a point on the y-axis. M(–5, –7) is the mid-point of the line segment joining P(p, –2) and Q. Find the value of p and the coordinates of Q. [(0, –12)] 5. Referring to the figure, PQ is a diameter of a circle. (a) Find the coordinates of the centre C of the circle. (b) It is given that R(–5, 7) and S are the end points of the diameter RS of the circle. Find the coordinates of S. [(–2, 5)] [(1, 3)] 4 如果唔係 1 : 1 6. The figure shows two points A(–2, –4) and B(4, 5). P lies on AB such that AP : PB = 2 : 1 . Find the coordinates of P. 7. [(2, 2)] 36 Given that T(6, 2) lies on the line segment joining P(8, –5) and Qæç , 5 ö÷ , find PT : TQ . è 7 ø [7 : 3] 5 8. Referring to the figure, CQ is produced to meet the x-axis at D and CQ : QD = 2 : 3 . Find the value of c and the coordinates of D. 9. [(–4, 0)] In the figure, A and D are two points on the y-axis. B and C are two points on the x-axis. M(3, 4) and N(–3, –4) are the mid-points of AB and CD respectively. (a) Find the coordinates of A, B, C and D. (b) Determine whether AB and CD are parallel. 10. Referring to the figure, PQRS is a parallelogram and its diagonals intersect at M. Find the coordinates of P, M and R. [(0, 8); (6, 0); (–6, 0); (0, –8)] [Yes] [(0, 4); (5, 2); (10, 0)] 6 11. In the figure, the line segment joining A(10, –8) and B(6, y) cuts the x-axis at D, where AD = DB . The line segment joining A and C(x, –2) cuts the y-axis at E, where AE = EC . (a) (b) (i) Find the value of x and the coordinates of E. [–10; (0, –5)] (ii) Find the value of y and the coordinates of D. [8; (8, 0)] Show that DE = 1 BC . 2 7 12. Referring to the figure, AM is produced to meet the y-axis at B and AM = MB . N is a point on the xaxis such that NM ^ AB . (a) Find the value of m and the coordinates of B. [4; (0, 4)] (b) Find the coordinates of N. [(12, 0)] (c) If C and D are points on the x-axis such that AC // MN // BD, (i) find the coordinates of C and D, (ii) determine whether N is the mid-point of DC. [(20, 0); (4, 0)] [Yes] 8 13. The coordinates of A and B are (–7, 9) and (–2, –1) respectively. P(p, 3) is a point on AB. (a) Find AP : PB. [3 : 2] (b) Hence, find the value of p. [–4] 9 14. The line segment joining A(–5, –2) and B(8, 11) cuts the x-axis and the y-axis at P and Q respectively. (a) (i) Find AQ : QB. [5 : 8] (ii) Hence, find the coordinates of Q. [(0, 3)] (i) Find AP : PQ. [2 : 3] (ii) Hence, find the coordinates of P. [(–3, 0)] (b) (c) Find AP : PQ : QB. [2 : 3 : 8] 10 15. Referring to the figure, AC cuts the y-axis at Q and AQ = QC. P lies on AB and AB ^ AC . (a) Find the value of c and the coordinates of Q. [12; (0, 9)] (b) Find the values of b and p. [–11; –11] (c) Find AP : PB. [1 : 2] 11 16. Referring to the figure, ABCD is a parallelogram. P is a point on BC such that AP ^ BC an BP : PC = 1 : 3. (a) Find the coordinates of A and B. [(3, 7); (3, 2)] (b) Find the area of parallelogram ABCD. [40] 12 2.1 難少少啦 1. In the figure, the coordinates of A and B are (a, 0) and (0, b) respectively. If M is the mid-point of AB, prove that OM = 2. 1 AB . 2 In the figure, OABC is a rectangle, where OA = a units and OC = c units. P, Q, R and S are the midpoints of OA, AB, BC and OC respectively. Prove that PQRS is a rhombus. 13 3. It is given that OABC is a square of side a units. P, Q, R and S are points on OA, AB, BC and CO respectively, such that OP : PA = AQ : QB = BR : RC = CS : SO = 1 : 2. Prove that PR and QS bisect each other. Copyright © Gauss Mathematics Education Centre. All rights reserved. 14