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.

Answer :

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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