Find the image of the point `(3, 8)`with respect to the line `x + 3y = 7`assuming the line to be a plane mirror.

Explanation

Let equation of line `PQ` is,
`x+3y=7`…….`(1)`
Let the image of `A-=(3,8)` in line `(1)` is `B(h,k)`, slope of line `PQ` is
`m_(1)=-(1)/(3)`
`:.` Slope of line `AB`, `m_(2)=-(1)/(m_(1))=3`
Equation of line `AB`,
`y-8=3(x-3)`
`implies y-8=3x-9`
`implies 3x-y=1`........`(2)`
Solving equations `(1)` and `(2)`
`x=1`, `y=2`
`:.`Coordinates of `R=(1,2)`
Which is the mid-point of line segment `AB`
Therefore, `(h+3)/(2)=1` and `(k+8)/(2)=2`
`impliesh=-1` and `k=-4`
`:.` Coordinates of image `=(-1,-4)`