can you please tell me if the points (8,9) (15,2) and (17,4) are the vertices of a right triangle

Answer 1

The lengths L of three sides are sqrt 98, sqrt 8 and sqrt 106. You can prove that using
L = sqrt[(y2-y1)^2 + (x2-x1)^2]
The pythagorean relationship a^2 + b^2 + c^2 is therefore obeyed, since 98 + 9 = 106.
What does that tell you about the triangle?

You could prove it in other ways, but this appeared to be the simplest.

Answer 2

so tey are vertices of a triangle?