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Question

The centroid of a triangle is (2,7) and two of its vertices are (4, 8) and (2, 6). The third vertex is


A

(0, 0)

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B

(4, 7)

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C

(7, 4)

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D

(7, 7)

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Solution

The correct option is D

(4, 7)


Let A(4, 8) and B(2, 6) be the given vertex. Let C(h, k) be the third vertex.

The centroid of ΔABC is (42+h3,8+6+k3)

It is given that the centroid of triangle ABC is (2, 7).

42+h3=2,8+6+k3=7

h=4, k=7

Thus, the third vertex is (4, 7)


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