Question

If the point $A$ is symmetric to the point $B(4,-1)$ with respect to the bisector of the first quadrant, then the length of $AB$ is

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

Answer 1

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

The line $y=x$ is known as the bisector of first quadrant.
Now image of $B(4,-1)$ in the line $y=x$ will be $A(-1,4)$


$\therefore AB=\sqrt{(-1-4{)}^2+(4+1{)}^2}=5\sqrt{2}$ units