Q20 of 184 Page 10

The coordinates of the centroid of a triangle are (√3,2), and two of its vertices are (2√3,-1) and (2√3,5). Find the third vertex of the triangle.

Let the third vertex of a triangle be (x, y)


Here, x1 = 2√3, x2 = 2√3, x3 = x


and y1 = -1, y2 = 5, y3 = y


and the coordinates of the centroid is (√3, 2)


We know that






⇒ 4√3 + x = 3√3 and 4 + y = 6


⇒ x = -√3 and y = 2


Hence, the third vertex of a triangle is (-√3, 2)


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