Problem B

Triangular Fun

Work through the parts that follow using the following coordinate plane, where grid lines are spaced \(1\) unit apart.

Label the coordinates of the points \(A\), \(O\), and \(B\).

Plot point \(C\) on the \(y\)-axis so that \(OC\) is twice the length of \(OA\). Then plot point \(D\) on the \(x\)-axis so that \(OD\) is twice the length of \(OB\). Label the coordinates of points \(C\) and \(D\).

Show that the area of \(\triangle COD\) is four times the area of \(\triangle AOB\). To show this, you may use your diagram or an area formula.

**Extension:** In
general, if you double the lengths of the two perpendicular sides of any
right-angled triangle, will the area of the new triangle be four times
the area of the original triangle? Explain.

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**Theme: **Geometry & Measurement