Three sides AB, BC and CA of a triangle ABC are 5x – 3y + 2 = 0, x – 3y – 2 = 0 and x + y – 6 = 0 respectively. Find the equation of the altitude through the vertex A.

Given:

The sides AB, BC and CA of a triangle ABC are as follows:

5x − 3y + 2 = 0 … (1)

x − 3y − 2 = 0 … (2)

x + y − 6 = 0 … (3)

To find:

The equation of the Altitude through the vertex A.

Concept Used:

Point of intersection of two lines.

Explanation:

Solving (1) and (3):

x = 2 , y = 4

Thus, AB and CA intersect at A (2, 4).

Slope of AD × Slope of BC = −1

Here, slope of BC = slope of the line (2) = 1/3

Slope of AD×1/3 = - 1 Slope of AD = - 3

Hence, the equation of the altitude AD passing through A (2, 4) and having slope −3 is y - 4 = - 3x - 2 3x + y = 10

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
Understand The Interesting Concept Of Relative velocity in 1- Dimension44 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