Question

Are the points (1,1),(13,1), (13,6) the points of the vertices of a triangle?

Answer 1

Let the points be A(1,1) , B(13,1) and C(13,6).

By Distance Formula, 

AB² = (1 - 13)² + (1 - 1)²
       = (-12)² + 0²
       = 144 + 0
∴AB² = 144


BC² = (13 - 13)² + (1 - 6)²
       = 0² + (-5)²
       = 0 + 25
∴BC² = 25


AC² = (1 - 13)² + (1 - 6)²
       = (-12)² + (-5)²
       = 144 + 25
∴AC² = 169

Now, AB² + BC² = 144 + 25
                          = 169
                          = AC²

∴AB² + BC² = AC²

Thus, (1,1) , (13,1) and (13,6) are the vertices of a triangle, and that too a right angled triangle.

Answer 2

yes these are points are of a right angled triangle triangle.

we can check it using distance formula