Question

Point $A$ is symmetric to $B(4,-1)$ with respect to the bisector of the first quadrant. Find length of segment $AB$.

• A. $10\sqrt{2}$
• B. $5\sqrt{2}$
• C. $5\frac{\sqrt{2}}{2}$
• D. $5$

Answer 1

The correct option is B $5\sqrt{2}$

Equation of bisector of first quadrant is $x=y$
Given $B(4,-1)$. So, its image w.r.t the line mirror $y=x$ is $A(-1,4)$.
Length $AB=\sqrt{25+25}=5\sqrt{2}$