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A B C is an isosceles triangle. If the c...

`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`

A

(1,6)

B

`(-1//2,5) `

C

`(-5//6,6) `

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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)`.
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Knowledge Check

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