Question

What is the image of the point (2, 3) in the line y = - x ?

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

Answer 1

Answer: (A)

Let there be a point P(2,3) on cartesian plane.
Image of this point in the line y = -x will lie on a line which is perpendicular to this line and distance of this point from y = -x will be equal to distance of the image from this line.
Let Q be the image of p and let the co-ordinate of Q be (b, k) Slope of line y = -x is -1
Line joining P, Q will be perpendicular to y = -x so, its slope = 1.
Let the equation of the line be y = x + c since this passes through point (2, 3)
3 = 2 + c $\to$ c = 1 and the equation y = x + 1
The point of intersection R lies in the middle of P & Q. Point of intersection of line y = - x and y = x + 1 is
$2y=1,\Rightarrow y=\frac{1}{2}$ and $x=-\frac{1}{2}$
Hence, $\frac{h+2}{2}=-\frac{1}{2}$ and $\frac{k+3}{2}=\frac{1}{2}$
$\Rightarrow h=-3$ and $k=-2$
So, the image of the point (2, 3) in the y = - x is ( -3, -2).