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Question

The line $$PQ$$ whose equation is $$x- y = 2$$ cuts the $$x-$$axis at $$P$$ and $$Q$$ and passes through$$(4,2)$$. The line $$PQ$$ is rotated about $$P$$ through $$45^o$$ in the anticlockwise direction. The equation of the line $$PQ$$ in the new position is


A
y=2
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B
y=2
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C
x=2
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D
x=2
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Solution

The correct option is C $$x=2$$
$$m_{PQ}=\dfrac {2-0}{4-2}=1$$
Now, PQ is rotated through $$45^o$$ about P in anticlockwise direction
$$\therefore$$ slope of PQ becomes infinity.
$$\therefore$$ Equation of PQ in new position is $$x = 2$$
256759_258352_ans_94daeb9c55774f76a5553d002cf81a51.png

Mathematics

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