how to find 3 sides(points) of a triangle given three equations as sides

Question

Given three equations, we must find three points like (1,0)(1,6)(3,5) as sides of a triangle.

Answer 1

Let  the points are

.

Slope of AB = .

The slope is undefined, so the vertical line AB is x = 1.

Slope of BC .

Point - slope form : .

Substitute the values of slope(m) = - 1/2 and in Point - slope form.

.

The line equation of BC is .

Slope of CA .

Point - slope form : .

Substitute the values of slope(m) = 5/2 and in Point - slope form.

.

The line equation of CA is .

Therefore the three equations of the triangle are x = 1, and .