Question

the cooridinate of the centroid are (1,3) and two of its vertices are (-7,6) and (8,5). find the third vertex. also find the coridinate of the centroid of the triangle when the third vertex is (2,4)

Answer 1

Hey... I think this can be ur answer!!
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A(-7,6)
B(8,5)
C(x,y)

G(1,3)
Now,

(1,3) = (-7+8+x/3 , 6+5+y/3)
(1,3) = (1+x/3 , 11+y/3)

3 = 1+x
x=2

And
9=11+y
y=-2

So coordinates of third vertex (2,-2)

Now let C(2,4)
A(-7,6)
B(8,5)

Now,
G(x,y) = (-7+8+2/3 , 6+5+4/3)
=(3/3 , 15/3)
=(1, 5)

So coordinates of centroid would be (1,5)

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Hope it helps you dear ☺️☺️☺️☺️