Question

A triangles is formed bt the lines y+x-6=0, 3y-x+2=0 and 3y=5x+2. find the coordinates of its orthocentre.

Answer 1

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)

աas tɦɨs aռsաɛʀ ɦɛʟքʄʊʟ .....
քʟʐ ʍaʀҡ as ɮʀaɨռɨɛst...