Cartesian equation of a triangle

Question

I am wondering what will be the equation of a triangle with vertices at (1,0), (0,-1), and (2,-1)?

I really appreciate your quick responses on this!

Shah

Answer 1

There is no single explicit equation that describes any triangle.

What you can do is find the equations of each of the three lines joining the vertices. The points of intersection of those lines, of course, are the given vertices.

Recall, given two points $(x_1, y_1), (x_2,y_2)$, the equation of the line that joins them is given by:

$$(y - y_1)=\underbrace{\left(\dfrac{y_2-y_1}{x_2-x_1}\right)}_{\text{slope}}(x - x_1)$$

So find the equation of the line joining $(1,0), (0,-1)$, the equation of the line joining $(0, -1)$ and $(2,-1)$, and the equation of the line joining $(2, -1)$ and $(1, 0)$. The triangle is then bounded by those three lines.