The vertices of a ΔABC and given by A(2, 3) and B(–2, 1) and its centroid is G Find the coordinates of the third vertex C of the ΔABC.
A. (0,2)
B. (1,-2)
C. (2,-3)
D. (-2,3)
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Answer:
Let A(3,2),B(−2,1) and C(x,y) be the coordintes of a triangle.
Centroid(
2
5
,
3
−1
)=(
3
3−2+x
,
3
2+1+y
)
Equating the x−co-ordiantes and y−co-ordinates we get
3
1+x
=
2
5
2+2x=15
or x=
2
13
And
3
3+y
=
3
−1
y+3=−1 or y=−4
∴ the coordinate C is (
2
13
,−4)
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