Question

On the Cartesian plane, PR = QR.
The possible coordinates of R are

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

Answer 1

The correct option is C (2,3)

$P\equiv (0,2)$

$Q\equiv (3,1)$

For option $A,R\equiv (1,-1)$

$PR=\sqrt{(0-1{)}^2+{(2-(-1\left)\right)}^2}=\sqrt{10}$

$QR=\sqrt{(3-1{)}^2+{(1-(-1\left)\right)}^2}=2\sqrt{2}$

$PR\ne QR$

For option $B,R\equiv (2,-1)$

$PR=\sqrt{(0-2{)}^2+{(-2-2)}^2}=\sqrt{20}$

$PR=\sqrt{(2-3{)}^2+{(-2-1)}^2}=\sqrt{10}$

$PR\ne QR$

For option $C$, $R\equiv (2,3)$

$PR=\sqrt{(2-0{)}^2+{(3-2)}^2}=\sqrt{5}$

$PR=\sqrt{(3-2{)}^2+{(3-1)}^2}=\sqrt{5}$

$PR=QR$

So, Option $C$ is correct.