# If (—2, 3), (4, —3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates of its centroid.

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

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Let A(x1,y1), B(x2,y2) and C(x3,y3), be the vertices of ΔABC

Let D(-2, 3), E(4, -3) and F(4, 5) be the midpoints of sides BC, CA and AB respectively

Since, D is the midpoint of BC

From (i), (ii) and (iii), we get

From (i) and (iv), we get

x1-4=6 and y1+6=5

x1=10, y1= -1

So, the coordinates of A are (10,-1)

From (ii) and (iv)

x2+8=6 and y2-6=5

x2= -2, y2=11

So, the coordinates of B are (-2,11)

From (iii) and (iv)

x3+8=6 and y3+10=5

x3= -2, y3= -5

So, the coordinates of C are (-2,-5)

Therefore, The vertices of ΔABC are A(10,-1), B(-2,11) and C(-2,-5)

Hence, coordinates of the centroid of ΔABC are