(D) Given point $P(1,5)$.The image of point $P(1,5)$ about the line $y=x$ is $Q(5,1)$.The image of point $Q(5,1)$ about the line $y=-x$ is $R(-1,-5)$.

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(D) Given point $P(1,5)$.The image of point $P(1,5)$ about the line $y=x$ is $Q(5,1)$.The image of point $Q(5,1)$ about the line $y=-x$ is $R(-1,-5)$.Since the lines $y=x$ and $y=-x$ are perpendicular, the angle $\angle PQR = 90^{\circ}$.Thus, $\Delta PQR$ is a right-angled triangle with the right angle at $Q$.The circumcentre of a right-angled triangle is the midpoint of its hypotenuse $PR$.Circumcentre $= \left(\frac{1+(-1)}{2}, \frac{5+(-5)}{2}\right) = (0,0)$.

Class 11 Mathematics Straight Line Foot of perpendicular, Image of a point and Reflexive properties

Medium

The point $Q$ is the image of the point $P(1,5)$ about the line $y=x$ and $R$ is the image of the point $Q$ about the line $y=-x$. The circumcentre of the $\Delta PQR$ is

WBJEE 2018 All WBJEE

A
$(5,1)$
B
$(-5,1)$
C
$(1,-5)$
D
$(0,0)$

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Straight Line

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Foot of perpendicular, Image of a point and Reflexive properties

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The point $Q$ is the image of the point $P(1,5)$ about the line $y=x$ and $R$ is the image of the point $Q$ about the line $y=-x$. The circumcentre of the $\Delta PQR$ is

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