Question

prove that the area of a triangle whose vertices are (-5,1) , (3,2) AND (5,7) is 4 times the word area of the triangle formed by the lines joining midpoints of the sides​

Answer 1

Answer:

Correct option is

C

32 square units

Area of a triangle with vertices (x

1

,y

1

) ; (x

2

,y

2

) and (x

3

,y

3

) is

∣

∣

∣

∣

∣

2

x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)

∣

∣

∣

∣

∣

Hence, substituting the points (x

1

,y

1

)=(−5,−1) ; (x

2

,y

2

)=(3,−5) and (x

3

,y

3

)=(5,2) in the area formula, we get

Area of triangle ABC =

∣

∣

∣

∣

∣

2

(−5)(−5−2)+(3)(2+1)+5(−1+5)

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

2

35+9+20

∣

∣

∣

∣

∣

=

2

64

=32squnits