Write the c

Given:

Line x + 3y – 7 = 0, point (3, 8).

To find:

The coordinates of the image.

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 that lies on the line x + 3y − 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

⇒

⇒ 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).