Question

ABC is an isosceles triangle. If the coordinates of the base are B (1,3) and C (- 2, 7), the coordinates of vertex

A can be

• A. (1, 6)
• B.
• C.
• D. None of these

Answer 1

The correct option is C

The vertex A(x, y) is equidistant from B and C because ABC is an isosceles triangle. Therefore,

$(x-1{)}^2+(y-3{)}^2=(x+2{)}^2+(y-7{)}^2$

$\Rightarrow$ 6x - 8y + 43 = 0

Thus, any point lying on this line can be the vertex A except the mid-point $(-\frac{1}{2},5)$ of BC.
note: A lies on perpendicular bisector of BC