# Find the orthocenter of the triangle the equations of whose sides are x + y = 1, 2x + 3y = 6 and 4x – y + 4 = 0.

Given: Sides of triangle are are x + y = 1, 2x + 3y = 6 and 4x – y + 4 = 0.

Assuming: AB, BC and AC be the sides of triangle whose equation is are x + y = 1, 2x + 3y = 6 and 4x – y + 4 = 0.

To find:

Orthocenter of triangle.

Concept Used:

Point of intersection of two lines.

Explanation:

x + y – 1 = 0 …… (i)

2x + 3y – 6 = 0 …… (ii)

4x – y + 4 = 0. …… (iii)

By solving equation (i) and (ii) By cross multiplication

x = - 3 ,y = 4

B( - 3, 4)

By Solving equation (i) and (iii) By cross multiplication

x , y

A

Equation of BC is 2x + 3y = 6

Altitude AD is perpendicular to BC,

Therefore, equation of AD is x + y + k = 0

k = - 1

Equation of AD is x + y – 1 = 0 …… (iv)

Altitude BE is perpendicular to AC.

Let the equation of DE be x – 2y = k

BE is passing through D( - 3, 4)

- 3 – 8 = k

k = - 11

Equation of BE is x – 2y = - 11 …… (v)

By solving equation (iv) and (v),

We get, x = - 3 and y = 4

Hence, the orthocenter of triangle is ( - 3, 4).

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
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Parametric Equations of Straight line48 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