Raffles Institution 2024 Y3 SUPP WS Coordinate Geometry

Page 1 of 8 RAFFLES INSTITUTION MATHEMATICS DEPARTMENT 2024 YEAR 3 RP MATHEMATICS TOPIC 5: COORDINATE GEOMETRY (MATHS 1 & MATHS 2) SUPPLEMENTARY WORKSHEET Name: Class: 3 ( ) Date: 1 2022/Y3RP/M2/T1/Q3 The equation of a circle, 1C , with centre A , is 22 6 4 87xy xy+−−= . (i) Find the coordinates of A and the radius of 1C . [3] (ii) The point ( )11, 8P lies on 1C . Find the equation of the tangent to 1C at P . [2] (iii) Determine if the point ( )9, 7Q − lies inside 1C . Justify your answer. [2] [Ans: (i) A(3, 2), 10 units (ii) 4 68 33yx= −+ (iii) No] 2 2022/Y3RP/M2/T1/Q4 The diagram shows a right-angled triangle OBC , where O is the origin and the point C is at ( )10, 0 . OB is perpendicular to BC and the equation of BC is 2 20yx= −+ . Point D lies on BC produced such that : 7:2BD CD = . (i) Show that the coordinates of point B are (8, 4). [2] (ii) Find the coordinates of D .[2] (iii) Explain why it is possible to draw a circle passing through O , B and D . [1] (iv) Given that point A is a reflection of point B in the x- axis, find the area of triangle ACD . [3] [Ans: (ii) 4310 , 155D − (iv) 13 5 units2] 3 2021/Y3RP/M2/T1/Q2 Solution to this question by accurate drawing will not be accepted. The diagram shows an isosceles triangle ABC with vertices A( )3,1 and B( )2,3− and AB AC= . The equation of the line BC is 3 27 7 0xy+−= . Find (i) the equation of the perpendicular bisector of BC, [2] (ii) the coordinates of the mid-point, M, of BC, [3] (iii) the area of triangle ABC. [2] (iv) the coordinates of the point P which lies on AB produced such that : 2:3AB AP = . [2] [Ans:(i) 7 83yx= −+ (ii) 111 ,422   (iii) 114 2 units2(iv) 14 , 42 − ]

Page 2 of 8 4 2021/Y3RP/M2/T1/Q5 A circle passes through the points ( )3, 0A and ( )1, 8B − . The x -axis is a tangent to the circle at A. (i) Explain briefly why the x-coordinate of the centre of the circle is 3. [1] (ii) Find the equation of the circle. [3] [Ans: (ii) ( ) ( ) 22 3 52xy− +− = ] 5 2020/Y3RP/M2/T1/Q4 Solutions to this question by accurate drawing will not be accepted. The diagram shows a circle 22 2 4 20 0xy xy+++−= with centre G . TA and TB are tangents to the circle at A and B respectively from point ( )14, 8T − . (i) State the centre G of the circle. [1] (ii) Find the length of GT , leaving your answer in surd form. [2] (iii) Explain why GT is the diameter of the circle that passes through the points ,,AG B and T . Hence, find the equation of this circle. [3] [Ans: (i) ( )1, 2−− (ii) 3 29 units (iii) ( ) 2 213 261524xy − ++ = ] 6 2020/Y3RP/M2/T1/Q5 Solutions to this question by accurate drawing will not be accepted. In the diagram, ABCD is a parallelogram in which C is ( )1,