find co ordinates of vertices of the triangke if co ordinatrzof midpoints of side of yriangle are a3, 2 4, 4 1, 3 andb 3, 4 4, 1 and2, 0
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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)
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