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The image of \mathrm{P}(\mathrm{a}, \mathrm{b}) on \mathrm{y}=-\mathrm{x} is \mathrm{Q} and the image of \mathrm{Q} on the line \mathrm{y}=\mathrm{x} is \mathrm{R}. Then the mid point of \mathrm{PR} is

Option: 1

\mathrm{(a+b, b+a)}


Option: 2

\left(\frac{\mathrm{a}+\mathrm{b}}{2}, \frac{\mathrm{b}+\mathrm{a}}{2}\right)


Option: 3

\mathrm{(a-b, b-a)}


Option: 4

(0,0)


Answers (1)

best_answer

The image of \mathrm{P}(\mathrm{a}, \mathrm{b}) on \mathrm{y}=-\mathrm{x} is \mathrm{Q}(-\mathrm{b},-\mathrm{a}) (interchange and change signs) and the image of \mathrm{Q}(-\mathrm{b},-\mathrm{a}) on \, \mathrm{y}=\mathrm{x} is \mathrm{R}(-\mathrm{a},-\mathrm{b}) (merely interchanges).

\therefore The mid point of PR is (0,0).

 

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Rishabh

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