The diagram shows a triangle $ABC$ in which $A$ is $(0,\ 6)$, $B$ is $(a,\ 7)$ and $C$ i

Question

The diagram shows a triangle $ABC$ in which $A$ is $(0,\ 6)$, $B$ is $(a,\ 7)$ and $C$ is $(12,\ 0)$. The point $M$ is the midpoint of $AC$ and $BM$ is perpendicular to $AC$. Find the coordinates of $M$,[1] the equation of the perpendicular bisector of $AC$,[3] the value of $a$,[2] the area of the triangle $ABC$.[3]

Accepted Answer

(i) $M=(6,3)$ (ii) $y=2x-9$ (iii) $a=8$ (iv) $30\text{ units}^2$

Perpendicular bisector of a side of a triangle

Perpendicular bisector of a side of a triangle

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