The diagram shows a rectangle $ABCD$ in which $A$ and $C$ lie on the $x$-axis. The equation

Question

The diagram shows a rectangle $ABCD$ in which $A$ and $C$ lie on the $x$-axis. The equation of $AB$ is $3y=x+1$ and the equation of $BD$ is $4y=3x-12$. Find the coordinates of $B$,[2] the coordinates of the midpoint of $AC$,[2] the coordinates of $A$, $C$ and $D$,[4] the length of $BC$,[2] the area of the rectangle $ABCD$.[2]

Accepted Answer

(i) $B=(8,3)$ (ii) $(4,0)$ (iii) $A=(-1,0)$, $C=(9,0)$, $D=(0,-3)$ (iv) $\sqrt{10}\text{ units}\approx3.16\text{ units}$ (3 s.f.) (v) $30\text{ units}^2$

Rectangle with a diagonal along the x-axis

Rectangle with a diagonal along the x-axis

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