Write the coordinates of the image of the point `(3,8)` in the lines `x+3y-7=0.`

Explanation

Let the given point be A(3,8) and its image in the line x + 3y − 7 = 0 is B(h,k).

The midpoint of AB is (3+h)/2,(8+k)/2 that lies on the line x + 3y − 7 = 0

∴`( 3+h)/2 + 3 xx (8+k)/2 - 7 = 0`

`h + 3k + 13 = 0` … (1)

AB and the line `x + 3y − 7 = 0` are perpendicular.

∴Slope of AB × Slope of the line =` - 1`

⇒ `(k−8)/(h−3) x −1/3 = -1`

⇒ `3h – k – 1 = 0 `… (2)
Solving (1) and (2), we get:`(h, k) = (− 1, − 4) `
Hence, the image of the point (3,8) in the line` x + 3y − 7 = 0` is` (− 1, − 4)`.