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Problem of the Week
Problem B
Triangular Fun

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

The coordinate plane with horizontal axis pointing to the right labelled x, and vertical axis pointing up labelled y. The two axes meet at point O. There are eight vertical and eight horizontal grid lines. Point A is on the vertical axis, 4 units above O. Point B is on the horizontal axis, 3 units to the right of O. Triangle AOB is highlighted.

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

  2. 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 \(D\).

  3. 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