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

Options

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

Answer

B

Explanation

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 (h, 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 implies 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, implies y=1/2 and x=-1/2`
Hence, `(h+2)/2=- 1/2 and (k+3)/2=1/2`
`implies h=-3 and k=-2`
So, the image of the point (2, 3) in the line `y=-x` is (-3, -2).