Q.

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 ________ .

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answer is 19.

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Detailed Solution

ADDE=BDDC=ABAC∴ D≡13,13 and E=(−2,0) Area of △ACE+ Area of △ABC=2× Area of △ACE=2×192 sq.units
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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 ________ .