Q. 105.0( 1 Vote )

# 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).

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