$ABCD$ is a rhombus in which $A$ is $(4,\ 6)$ and $B$ is $(5,\ 14)$. The diagonals $AC$

Question

$ABCD$ is a rhombus in which $A$ is $(4,\ 6)$ and $B$ is $(5,\ 14)$. The diagonals $AC$ and $BD$ intersect at $T$, and $AC$ cuts the $y$-axis at $(0,\ 4)$. Find the equations of $AC$ and $BD$.[4] Calculate the coordinates of $T$, $C$ and $D$.[4] Find the area of the rhombus $ABCD$.[3]

Accepted Answer

(i) $AC:\ 2y=x+8$, $BD:\ y=-2x+24$ (ii) $T=(8,8)$, $C=(12,10)$, $D=(11,2)$ (iii) $60\text{ units}^2$

Diagonals of a rhombus

Diagonals of a rhombus

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