Question

On the Cartesian plane, P, Q and R are vertices of an isosceles triangle
Which of the following are the possible coordinates of R?

• A. (-1, 2)
• B. (1,-2)
• C. (1, 4)
• D. (3, -2)

Answer 1

The correct option is B (1,-2)

since triangle is isosceles,Thus altitude will be its median where median is not on either of equal sides, Thus the abscissa of coordinate of third series will be equal to that of abscissa of mid point of P,Q, since R lies on median

and as $P\equiv (-2,2)$

$Q\equiv (3,2)$

mid point$\equiv (\frac{1}{2},2)$

so, coordinate of R $\equiv (\frac{1}{2},K)$ where $K\in R$