# Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x – 4y + 8 = 0.

Given: (x1,y1) = A(2,5)

To find:

The distance of a point from the line parallel to another line.

Explanation:

It is given that the required line is parallel to 3x −4y + 8 = 0

4y = 3x + 8

y

tanθ

sinθ, cosθ

So, the equation of the line is

3x – 6 = 4y – 20

3x – 4y + 14 = 0

Let the line 3x – 4y + 14 = 0 cut the line 3x + y + 4 = 0 at P.

Let AP = r Then, the coordinates of P are given by

x, y

Thus, the coordinates of P are

Clearly, P lies on the line 3x + y + 4 = 0.

r = – 5

AP = |r| = 5

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of line45 mins
Parametric Equations of Straight line48 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 1169 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses