Question

Point $Q$ is symmetric to $P(4,-1)$ with respect to the bisector of the first quadrant. The length of $PQ$ is

• A. $3\sqrt{2}$
• B. $5\sqrt{2}$
• C. $7\sqrt{2}$
• D. $9\sqrt{2}$

Answer 1

Answer: (B)

$5\sqrt{2}$

Equation of the bisector of the first quadrant $y=x$
The coordinates of point $Q$ which is symmetric to $P(4,-1)$ is $(-1,4)$
$\therefore PQ=\sqrt{{(4+1)}^2+{(-1-4)}^2}=\sqrt{25+25}=5\sqrt{2}$