Coordinate Geometry

Question 9: Solution by scale drawing is not accepted. Diagram 3 shows three points, A, B and D in a Cartesian plane. The straight line AB is perpendicular to straight line BD which intersect the y-axis at D. The equation of the line BD is y = 2x – 5. (a) Find the equation of the … Read more

Question 7: Solutions by scale drawing will not be accepted. Diagram below shows a triangle OPQ. Point S lies on the line PQ. (a) A point Y moves such that its distance from point S is always 5 uints. Find the equation of the locus of Y.   (b) It is given that point P and point … Read more

Question 5: In the diagram, the equation of FMG is y = – 4. A point P moves such that its distance from E is always half of the distance of E from the straight line FG. Find (a) The equation of the locus of P, (b) The x-coordinate of the point of intersection of … Read more

Question 3: In the diagram, PRS and QRT are straight lines. Given R is the midpoint of PS and QR : RT = 1 : 3, Find (a) the coordinates of R, (b) the coordinates of T, (c) the coordinates of the point of intersection between lines PQ and ST produced. Solution: (a) Given R is the … Read more

Question 1: The diagram shows a straight line PQ which meets a straight line RS at the point Q. The point P lies on the y-axis. (a) Write down the equation of RS in the intercept form. (b) Given that 2RQ = QS, find the coordinates of Q. (c) Given that PQ is perpendicular to … Read more

Question 6: The point M is (–3, 5) and the point N is (4, 7). The point P moves such that PM: PN = 2: 3. Find the equation of the locus of P. Solution: Let  P = ( x , y ) P M : P N = 2 : 3 P M P … Read more

Question 3: The equation of the straight lines CD and EF are 5x + y – 4 = 0 and x 7 − y h = 1 . If CD and EF are parallel, find the value of h. Solution: Two parallel lines have same gradient.  5x + y – 4 = 0    y … Read more

Question 1: The vertices of a triangle are P (6, 1), Q (5, 6) and R (m, -1). Given that the area of the triangle is 31 unit2, find the values of m. Solution: Area of  △   P Q R  =  31 1 2   | 6  5    m   1  6 − 1 … Read more

7.6 Equation of a Locus 1. The equation of the locus of a moving point P(x, y) which is always at a constant distance (r) from a fixed point (x1, y1) is: 2. The equation of the locus of a moving point P(x, y) which is always at a constant distance from two fixed points (x1, … Read more

7.5 Parallel Lines and Perpendicular Lines (A) Parallel Lines 1. If two straight lines are parallel, they have same gradient. In the above diagram, if straight line L1 is parallel to straight line L2, gradient of L1 = gradient of L2 m 1 = m 2 Example 1: Given that the equation of a straight line parallel to x + 8y= 40 … Read more