Question

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

Answer 1

Answer:

Let the coordinates of the third vertex be (x, y). Then,

3x+3−7=2and 3y−5+4 =−1⇒x−4=6andy−1=−3⇒x=10andy=−2

Thus,the coordinates of the third vertex are (10, -2).

Answer 2

Answer:

The coordinates of centroid (x,y) of a triangle are

$\frac{x1+x2+x3}{3}$

$\frac{y1+y2+y3}{3}$

In the given problem,

(x1,x2)=(3,−5)

(x2,y2)=(−7,4)

(x2,y3)=?

(x,y)=(2,−1)

2=3-7+$x^{3}$/3

6=−4+x3

x3=6+4=10

And

-1=$\frac{-5+4+y3}{3}$

−3=−1+y3

y3 =−3+1=−2

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