Write the coordinates of the image of the point (3, 8) in the line x + 3y – 7 = 0.
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).