G6 - COORDINATE GEOMETRY PRACTICE

COORDINATE GEOMETRY PRACTICE 1. Given the equation of a straight line , find 2 𝑥 + 4 𝑦 = 24 (a) the gradient of the line [2] (b) the y-intercept of the line [1] 2. If a point R lies on the line , find the coordinates of R. 𝑚 ,− 2 𝑚 ( ) 3 𝑥 − 𝑦 = 5 [3] 3. Given the points P , Q and R 2 , 3 ( ) − 1 ,− 1 ( ) − 6 ,− 1 ( ) (a) write down the coordinates of S such that PQRS forms a parallelogram [1] (b) find the distance between points P and Q [2]

ANSWER SCHEME 1. Given the equation of a straight line , find 2 𝑥 + 4 𝑦 = 24 (a) the gradient of the line 2 𝑥 + 4 𝑦 = 24 4 𝑦 = 24 − 2 𝑥 , where is the gradient and is the y-intercept when . 𝑦 = 𝑚𝑥 + 𝑐 𝑚 𝑐 𝑥 = 0 𝑦 = 6 − 1 2 𝑥 𝑚 =− 1 2 [2] (b) the y-intercept of the line sub to 𝑥 = 0 𝑦 = 6 − 1 2 𝑥 𝑦 = 6 [1]

2. If a point R lies on the line , find the coordinates of R. 𝑚 ,− 2 𝑚 ( ) 3 𝑥 − 𝑦 = 5 R 𝑚 ,− 2 𝑚 ( ) R 𝑥 , 𝑦 ( ) → 3 𝑥 − 𝑦 = 5 3 𝑥 − 5 = 𝑦 Sub to 𝑥 = 𝑚 , 𝑦 =− 2 𝑚 3 𝑥 − 5 = 𝑦 − 2 𝑚 = 3 𝑚 − 5 − 5 𝑚 =− 5 𝑚 = 1 Coordinates of R 1 ,− 2 ( ) [3]

3. Given the points P , Q and R 2 , 3 ( ) − 1 ,− 1 ( ) − 6 ,− 1 ( ) (a) write down the coordinates of S such that PQRS forms a parallelogram Distance of R from Q − 6 +− 1 =− 5 5 units 2 − 5 =− 3 S − 3 , 3 ( ) (b) find the distance between points P and Q P , Q 2 , 3 ( ) − 1 ,− 1 ( ) Distance formula = 𝑥 2 − 𝑥 1 ( ) 2 + 𝑦 2 − 𝑦 1 ( ) 2 Distance = 2 −(− 1 )( ) 2 + 3 −( 1 )( ) 2 Distance = 5 units