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Problem 160

Geometry Difficulty 1.2 Multiple choice CEMC Fermat · Canada · 2022

In the diagram, points $P(2,6)$ , $Q(2,2)$ and $R(8,5)$ form a triangle.The area of $\triangle PQR$ is

Pick one

Official solution

The given triangle can be considered to have base $PQ$ (which is vertical along the line $x=2$ ) and perpendicular height which runs from $R$ horizontally to $PQ$ . The line segment joining $P(2,6)$ to $Q(2,2)$ has length 4. Point $R(8,5)$ is 6 units to the right of the line with equation $x =
2 $. Thus,$ $\triangle$ PQR $has area$ $\frac{1}{2}\cdot 4 \cdot$ 6 = 12$.

Figure for this problem

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