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Question

In an isosceles ΔABC, AB = AC. If BC is parallel to y-axis, coordinates of vertex B and centroid of ΔABC are (–5, 2) and (–4, –2) respectively, then the coordinates of vertex A when –6 is ordinate of vertex C are

A
(2, 2)
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B
(2, -2)
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C
(-2, 2)
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D
(-2, -2)
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Solution

The correct option is D (-2, -2)
Given that ΔABC is an isosceles triangle.

Therefore, AD is the perpendicular bisector as well as median of BC.

Since BC is parallel to y-axis, abscissa of vertex C in equal to abscissa of vertex B

Therefore, the coordinates of C are (–5, –6).

Let the coordinates of A be (x, y).



Let G be the centroid of ΔABC.

x+(5)+(5)3=4 and y+2+(6)3=2

x=2 and y=2

Thus, the coordinates of A are (–2, –2).

Hence, the correct answer is option (d).

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