The diagram shows a triangle $ABC$ with vertices $A(-4,\ 1)$, $B(2,\ 13)$ and $C(10,\ 5)$. T

Question

The diagram shows a triangle $ABC$ with vertices $A(-4,\ 1)$, $B(2,\ 13)$ and $C(10,\ 5)$. The point $M$ is the midpoint of $AB$ and the point $N$ is the midpoint of $BC$. [Diagram] (a) Find the coordinates of $M$ and of $N$. (b) Explain why the quadrilateral $ACNM$ is a trapezium. (c) Find the area of the quadrilateral $ACNM$.

Accepted Answer

(a) $M=(-1,7)$, $N=(6,9)$ (b) $MN\parallel AC$ but $AM\not\parallel CN$, so $ACNM$ is a trapezium (c) $54\text{ units}^2$

Trapezium cut from a triangle by two midpoints

Trapezium cut from a triangle by two midpoints

Solution:

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