Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Write the Coordinates of the Image of the Point (3, 8) in the Line X + 3y − 7 = 0. - Mathematics

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

#### Solution

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 $\left( \frac{3 + h}{2}, \frac{8 + k}{2} \right)$ that lies on the line x + 3y − 7 = 0.

$\therefore \frac{3 + h}{2} + 3 \times \frac{8 + k}{2} - 7 = 0$

$h + 3k + 13 = 0$         ... (1)

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

$\therefore\text { Slope of AB } \times \text { Slope of the line } = - 1$

$\Rightarrow \frac{k - 8}{h - 3} \times \frac{- 1}{3} = - 1$

$\Rightarrow 3h - k - 1 = 0$       ... (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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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Q 10 | Page 132