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