Question

If (- 2, 3),( 4, - 3) and (4,5) are the midpoints of the sides of a triangle find coordinates of its centroid

Answer 1

(x1 + x2 + x3 ÷ 3 ,. y1 + y2 + y3 ÷ 3)
( -2 + 4 + 4 ÷ 3 , 3 -3 + 5÷3)
(-2 + 8 ÷ 3 , 5 ÷ 3)
(2 , 5÷3) is the coordinate of the centroid.
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Answer 2

Answer: $(2,\dfrac{5}{3})$

Step-by-step explanation:

The centroid of a triangle and the centroid by the mid points of that triangle is same

As given (- 2, 3), ( 4, - 3) and (4,5) are the mid points

Now as we know,

$(x,y)=(\dfrac{x_1+x_2+x_3}{3} ,\dfrac{y_1+y_2+y_3}{3})\\\\=(\dfrac{-2+4+4}{3} ,\dfrac{3+(-3)+5}{3} )\\\\=(\dfrac{6}{3} ,\dfrac{5}{3}) = (2,\dfrac{5}{3})$

Hence, the coordinates  of the centroid is  $(2,\dfrac{5}{3})$