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A triangle ABC has vertices A5,1,B−1,−7, and C1,4 respectively. L be the line mirror passing through C and parallel to AB. A light 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 ΔACE and ΔABC is

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answer is 37.5.

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Detailed Solution

ADDE=BDDC=ABAC=2∴  D≡13,13 and E≡−2,0Area of ΔACE+ Area of ΔABC=252+25=37.5sq.units
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A triangle ABC has vertices A5,1,B−1,−7, and C1,4 respectively. L be the line mirror passing through C and parallel to AB. A light 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 ΔACE and ΔABC is