The diagram shows a rectangle $ABCD$ in which $A$ is $(1,\ 2)$ and $D$ is $(5,\ 0)$. The d

Question

The diagram shows a rectangle $ABCD$ in which $A$ is $(1,\ 2)$ and $D$ is $(5,\ 0)$. The diagonal $AC$ lies on the line $y=x+1$. Find the equation of $CD$,[3] the coordinates of $C$ and of $B$,[4] the length of $AB$,[2] the area of the rectangle $ABCD$.[2]

Accepted Answer

(i) $y=2x-10$ (ii) $C=(11,12)$, $B=(7,14)$ (iii) $6\sqrt5\text{ units}\approx13.4\text{ units}$ (3 s.f.) (iv) $60\text{ units}^2$

Rectangle from a vertex pair and a diagonal

Rectangle from a vertex pair and a diagonal

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