Question

Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex.

Answer 1

3rd vertex of the triangle is (-4, -7)

we know, centroid of triangle formed by joining the points (x₁, y₁) , (x₂, y₂) and (x₃, y₃) is [(x₁ + x₂ + x₃)/3 , (y₁ + y₂ + y₃)/3 ]

here two points are (1, 2) and (3, 5) .

let the third point is (x, y)

then, centroid is [(x + 1 + 3)/3 , (y + 2 + 5)/3]

= [(x + 4)/3, (y + 7)/3 ]

given centroid = (0, 0)

so, (x + 4)/3 = 0 ⇒x = -4

and ( y + 7)/3 = 0 ⇒y = -7

hence third vertex of the triangle is (-4, -7)

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