Question

On the Cartesian plane, $P,Q,$ and $R$ are vertices of an isosceles triangle.
Which of the following is tho possible coordinates of $R$

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

Answer 1

The correct option is B $(1,-2)$

Given points P (-2, 2), Q (3, 2), let R (x, y)

From distance formula

$PQ=\sqrt{(3-(-2){)}^2+(2-2{)}^2}$

$=5$

$PR=\sqrt{(x-(-2){)}^2+(y-2{)}^2}$

$=\sqrt{(x+2{)}^2+(y-2{)}^2}$

In isosceles triangle, $PQ=PR$

$\Rightarrow 5=\sqrt{(x+2){)}^2+(y-2{)}^2}$

$\Rightarrow 5^2=(x+2{)}^2+(y-2{)}^2$

only option B is satsifying