TS EAMCET · Maths · Straight Lines
Let Q be the image of a point \(\mathrm{P}(1,2)\) with respect to the line \(x+y+1=0\) and R be the image of Q with respect to the line \(x-y-1=0\). If M and N are the midpoints of PQ and QR respectively, then \(\mathrm{MN}=\)
- A \(\sqrt{10}\)
- B 4
- C \(\sqrt{22}\)
- D 5
Answer & Solution
Correct Answer
(A) \(\sqrt{10}\)
Step-by-step Solution
Detailed explanation
\(P=(1,2)\) Line 1: \(x+y+1=0\) \(Q = \left(1 - 2 \frac{1(1)+1(2)+1}{1^2+1^2}, 2 - 2 \frac{1(1)+1(2)+1}{1^2+1^2}\right) = \left(1 - 2 \frac{4}{2}, 2 - 2 \frac{4}{2}\right) = (1-4, 2-4) = (-3,-2)\) Line 2: \(x-y-1=0\)…
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