WBJEE 2024 Math Paper

To determine the possible coordinates of the vertex A in an isosceles triangle ABC with base endpoints B(1,3) and C(−2,7), we need to find the coordinates that satisfy the property that AB=AC.
Let's calculate the distance between B(1,3) and potential coordinates of A, as well as between C(−2,7) and potential coordinates of A.
1. Option A: A(1,6)
Since AB≠AC, Option A is incorrect.
2. Option B : A(−‌

1

8

,5)
Since AB≠AC, Option B is incorrect.
3. Option C: A(‌

5

6

,6)
Since AB=AC, Option C is correct.
4. Option D: A(−7,‌

1

8

)
Since AB=AC, Option D is also correct.
Therefore, the correct coordinates of A can be Option C: A(‌

5

6

,6) or Option D: A(−7,‌

1

8

).