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Question

A(1, 2), B(4, 6) and C(8, 12) form the vertices of a triangle. Which of the following is not the coordinates of medians of triangle ABC?


A
(52,4)
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B
(6, 9)
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C
(92,7)
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D
(72,4)
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Solution

The correct option is D (72,4)

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

The coordinates of the midpoint of a line segment joining (x1,y1) and (x2,y2) are (x1+x22,y1+y22).

Substituting values of x1,x2,y1 and y2 , we get

Midpoint of AB = (1+42,2+62) = (52,4)

Midpoint of BC = 4+82,6+122 = (6, 9)

Midpoint of AC = 1+82,2+122 = (92,7)

Therefore, the only option which is not a median of the given triangle is (72,4).


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