Coordinate Geometry - Area of Rectilinear Figures

A triangular panel is designed on a coordinate grid. Each coordinate unit represents \(1\) centimetre.
One edge of the panel joins \(P(1,1)\) to \(Q(1,5)\). The third vertex, \(R\), lies at the intersection of\[y=9-2x \quad\text{and}\quad x=3.2.\] Answer the following on graph paper. Use a scale of \(2\) cm to represent \(1\) unit on each axis, with \(0\leq x\leq4\) and \(0\leq y\leq10\).

1. Draw the graph of \(y=9-2x\) for \(0\leq x\leq4\).

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2. Draw the line \(x=3.2\). Label the intersection \(R\), and state its coordinates.

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3. Plot \(P\) and \(Q\), and join the three vertices to show the panel.

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4. A student uses \(PQ\) as the base and says that the perpendicular height is the \(y\)-coordinate of \(R\). Explain the mistake and state the correct height.

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5. Calculate the area of the panel.

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