triangle is formed by joning three lines x+y-6=0,3y-x+2=0 and 3y=5x+2?find the orthocenter of the triangle?

Let ΔABC be formed by the intersection of lines:

Then the coordinates of the vertices of triangle can be found as:

Point A can be found by intersection of lines 1 and 2.

Equating the values of x,

Point A = (5, 1)

 

Point B can be found by intersection of lines 1 and 3.

Equating the values of x,

Point B = (2, 4)

 

Point C can be found by intersection of lines 2 and 3.

Equating the values of x,

Point C = (–1, –1)

Thus the triangle  ABC is:

where H is the orthocenter. (Orthocenter is the point of intersection of altitudes)

Now, to calculate the the orthocenter, you can proceed in the similar manner as shown in the following link.

https://www.meritnation.com/ask-answer/question/my-question-is-find-the-coordinates-of-orthocenter-of-the/straight-lines/473627

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