First slide

Cartesian plane

Question

A triangle ABC has vertices A(5, 1), B(-1, -7), and C(1,4),respectively. L be the line mirror passing through C and parallel to AB. Alight ray emanating from point A goes along the direction of the internal bisector of angle A, which meets the mirror and BC at E and D, respectively. Then the sum of the areas of $△ ACE$ and $ΔABC$ is ________ .

Moderate

Solution

$\begin{array}{l} \frac{AD}{DE} = \frac{BD}{DC} = \frac{AB}{AC} \\ ∴ D \equiv (\frac{1}{3}, \frac{1}{3}) and E = (- 2, 0) \end{array}$

$\begin{array}{l} Area of △ ACE + Area of △ ABC \\ = 2 \times Area of △ ACE \\ = 2 \times \frac{19}{2} sq . units \end{array}$

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