Cartesian plane

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Point Q is symmetric to P (4, -1) with respect to the bisector of the first quadrant. If the length of $P Q is k \sqrt{2},$ then $k =$

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Solution

It is given that the point Q is symmetric to P ( 4, -1) with respect to $y = x .$ So,coordinates of Q are(-1, 4).
$∴ P Q = \sqrt{(4 - (- 1))^{2} + (- 1 - 4)^{2}} = 5 \sqrt{2}$

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