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 $A B \neq A C$, Option $A$ is incorrect. 2. Option B : $A \left(-\frac{1}{8}, 5\right)$Since $AB \neq AC$, Option B is incorrect. 3. Option C: $A \left(\frac{5}{6}, 6\right)$Since $AB = AC$, Option C is correct. 4. Option D: $A \left(-7, \frac{1}{8}\right)$Since $AB = AC$, Option D is also correct.Therefore, the correct coordinates of $A$ can be Option C: $A \left(\frac{5}{6}, 6\right)$ or Option D: $A \left(-7, \frac{1}{8}\right)$.