Question

The image of the point P(4, 1) with respect to the line y=x-1 is .

• A. (2, 3)
• B. (2, -3)
• C. (-2, -3)
• D. (-2, 3)

Answer 1

The correct option is A (2, 3)

Let Q(x', y') be the image of the point P w.r.t. the line x-y-1 = 0.
$\Rightarrow \frac{x\text{'}-4}{1}=\frac{y\text{'}-1}{-1}=\frac{-2(4-1-1)}{[1^2+(-1{)}^2]}\Rightarrow x\text{'}-4=1-y\text{'}=-2\Rightarrow x\text{'}=2\mathrm{and}y\text{'}=3$