Question

if D(4,-6),E(3,-2), F(5,2) are the midpoints of ∆ABC then find the coordinates of ABC​

Answer 1

Answer:

D,E and F are the midpoint of AB,BC and AC.

We have mid point formula,

P(X,Y)=(

2

x

1

+x

2

,

2

y

1

+y

2

)

⇒

2

x+a

=3⇒x+a=6

⇒

2

y+b

=−2⇒y+b=−4

⇒

2

a+p

=−3⇒a+p=−6

⇒

2

b+q

=1⇒b+q=2

⇒

2

x+p

=4⇒x+p=8

⇒

2

y+q

=−3⇒y+q=−6

Consider, x+a=6 and a+p=−6

⇒x−6−p=6

⇒x−p=12,x+p=8

⇒p=8−10=−2

∴2x=20 ⇒x=10

∴ a=−10+6=−4

Now,

y+a=−6

⇒−b−4+q=−6

⇒−b+q=−6+4

⇒ q−b=−2 ⇒b−q=2

2b=4

⇒b=2

∴y=−4−2=−6

y+q=−6

⇒q=−6+6=0

∴ Coordinate of vertices of △ABC are

A(10,−6),B(−4,2),C(−2,0)