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A triangle ABC vertices A(5,1),B(-1,-7) ...

A triangle ABC vertices A(5,1),B(-1,-7) and C(1,4). 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 `Delta ACE and Delta ABC` is

A

17 sq. units

B

18 sq. units

C

`(50)/(3)` sq. units

D

20 sq. units

Text Solution

Verified by Experts

The correct Answer is:
C

`(AD)/(DE) =(BD)/(DC) =(AB)/(AC)`
`:.` Point `D ((1)/(3),(1)/(3))` and `E(-2,0)`.
Area of `DeltaADC +` Area of `DeltaBDE`
`=(25)/(3) +(25)/(3)`
`=(50)/(3)` sq. units
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