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

The correct option is B

$5\sqrt{2}$

Explanation for the correct option:

Finding the length:

The given point is $P(4,-1)$

And $Q$ is symmetric to $P(4,-1)$

Then coordinate of $Q$ be $(-1,4)$

We know that the equation of the bisector of the first quadrant is $y=x$

Therefore, the length of $PQ$

$$\begin{gathered} \sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2} \\ \Rightarrow \sqrt{{(4+1)}^2+{(-1-4)}^2} \\ \Rightarrow \sqrt{(25+25)} \\ \Rightarrow \sqrt{50} \\ \Rightarrow 5\sqrt{2} \end{gathered}$$

Thus, the length of $PQ$ = $5\sqrt{2}$ unit.

Hence, option (B) is the correct answer.