Q. 6 A

# Three vertices of a triangle are A(1, 2), B(-3, 6) and C(5, 4). If D, E, and C, respectively, show that the area of triangle ABC is four times the area of triangle DEF.

Given: ABC is a triangle with points (1, 2), (-3, 6), (5, 4)

To prove: The area of triangle ABC is four times the area of triangle DEF

We know that Area of triangle Then,

Area of triangle ABC   = 12

Now we have to find point D, E, F

Hence D is the midpoint of side BC then,

Coordinates of D  = (1, 5 )

Hence E is the midpoint of side AC then,

Coordinates of E  = (3, 3)

Hence F is the midpoint of side AB then,

Coordinates of F  = (-1, 4)

Area of triangle Now Area of triangle DEF   = 3

Therefore Area of ABC = 4 Area of DEF.

Hence, Proved.

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