Question
Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex. [2 MARKS]
Answer: Option A
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Concept : 1 Mark
Application : 1 Mark
Let the coordinates of the third vertex be (x, y).
We know that the coordinates of the centroid of a triangle whose vertices are
(x1,y1),(x2,y2) and (x3,y3) are
x1+x2+x33,y1+y2+y33
Given points are (3, –5) and (–7, 4) and centroid is (2, –1).
⇒x+3−73=2 and y−5+43=−1
⇒x−4=6 and y−1=−3
⇒x=10 and y=−2
Thus the coordinates of the third vertex are (10, -2).
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