TS EAMCET · Maths · Straight Lines
If \(Q\) and \(R\) are the images of the point \(P(2,3)\) with respect to the lines \(x-y+2=0\) and \(2 x+y-2=0\) respectively, then \(Q\) and \(R\) lie on
- A the same side of the line \(2 x+y-2=0\)
- B the opposite sides of the line \(2 x-y-2=0\)
- C the same side of the line \(x+y+2=0\)
- D the opposite sides of the line \(x-y+2=0\)
Answer & Solution
Correct Answer
(C) the same side of the line \(x+y+2=0\)
Step-by-step Solution
Detailed explanation
Let the coordinates of \(a=(h, k)\) \(\begin{aligned} & \frac{h-2}{1}=\frac{k-3}{-1}=\frac{-(2-3+2)}{2}=\frac{-1}{2} \\ & h=\frac{3}{2}, k=\frac{7}{2} \Rightarrow Q=\left(\frac{3}{2}, \frac{7}{2}\right) \end{aligned}\) Let \(R \equiv\left(x_1, y_1\right)\)…
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