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)
• B. (2, -2)
• C. (-2, 2)
• D. (-2, -2)

Answer 1

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.

$\therefore \frac{x+(-5)+(-5)}{3}=-4and\frac{y+2+(-6)}{3}=-2$

$\Rightarrow x=-2andy=-2$

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

Hence, the correct answer is option (d).