Q. 105.0( 1 Vote )

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

Answer :

__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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