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Question

Two vertices of a triangle are (3,-5) and (-7,4). If its centroid is(2,-1), then find the third vertex.


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Solution

Finding the third vertex of the triangle:

Let A (x1,y1) be the first vertex of the triangle having coordinates(3,-5),

B (x2,y2)be the second vertex of the triangle having coordinates(-7,4) and

C be the third vertex of the triangle having coordinates (x3,y3)

The coordinates of the centroid of a triangle =x1+x2+x33,y1+y2+y33

Therefore,(2,-1) =3+(-7)+x33,-5+4+y33

On equating x and y coordinates on both sides

2=-4+x33 and -1=-1+y33

6+4=x3 and -3+1=y3

x3=10 and -2=y3

Hence, the coordinates of the third vertex C(x3,y3) is(10,-2).


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