Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
Points $A$ and $B$ have coordinates $(1,3)$ and $(9,-1)$ respectively, and $D$ is the mid-point of $AB$. Point $C$ is located at $(x,y)$, where $x$ and $y$ are variables.
(i)[1]
State the coordinates for point $D$.
(ii)[1]
Given that $CD^2 = 20$, write an equation in terms of $x$ and $y$.
(iii)[3]
$AC$ and $BC$ are the same length. Find an equation involving $x$ and $y$ and show that it simplifies to $y = 2x - 9$.
(iv)[4]
By using the results from parts (ii) and (iii), and showing all required working, find the possible coordinates of $C$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Coordinates for $D$ are correct: $D=(5,1)$” …