If two vertices of a triangle are (1, 1, 1).(-2, 4, 1) and the centroid is the origin then find the third
vertex
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1
Answer:
Let the △ABC has vertices A=(x
1
,y
1
)=(−1,4),B=(x
2
,y
2
)=(5,2) and C=(x
3
,y
3
).
The centroid G=(
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
)=(0,−3)
Therefore,
3
−1+5+x
3
=0
⇒x
3
=−4
Also
3
4+2+y
3
=−3
⇒y
3
=−15
∴C=(x
3
,y
3
)=(−4,−15)
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