`A B C` 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) `(-1/2,5)` (c)`(5/6,6)` (d) none of these

Options

A. (1,6)
B. `(-1//2,5) `
C. `(-5//6,6) `
D. none of these

Answer

C

Explanation

Let the vetex of triangle be `A(x,y)`.
Then the vetex `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`
or `6x-8y+43=0`
Thus, any point lying on this line can be the vertex A is `(5//6,6)`.