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

# Find the Equation of a Line Which is Perpendicular to the Line Joining (4, 2) and (3, 5) and Cuts off an Intercept of Length 3 on Y-axis. - Mathematics

Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.

#### Solution

Let m be the slope of the required line.
Here, c = y-intercept = 3
Slope of the line joining the points (4, 2) and (3, 5) = $\frac{5 - 2}{3 - 4} = - 3$

It is given that the required line is perpendicular to the line joining the points (4, 2) and (3, 5).

$\therefore m \times \text { Slope of the line joining the points }\left( 4, 2 \right) \text { and } \left( 3, 5 \right) = - 1$

$\Rightarrow m \times \left( - 3 \right) = - 1$

$\Rightarrow m = \frac{1}{3}$

Substituting the values of m and c in y = mx + c, we get,

$y = \frac{1}{3}x + 3$

$\Rightarrow x - 3y + 9 = 0$

Hence, the equation of the required line is x $-$ 3y + 9 = 0

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.3 | Q 6 | Page 21