Mathematics 9709 · AS & A Level · Coordinate geometry

Coordinate geometry — practice question

Points $A$ and $B$ have coordinates $(-3k - 1,\ k + 3)$ and $(k + 3,\ 3k + 5)$ respectively, where $k$ is a constant $(k \neq -1)$.
(i)[2]

Find the gradient of $AB$ and simplify it fully, then show that it does not depend on $k$.

(ii)[5]

Find the equation of the perpendicular bisector of $AB$ and simplify it fully.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Gradient of $AB$ correctly simplified to $\frac12$” …

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI