Question

determine if the triangle with the vertices given is a right triangle; (-5,-4), (7,2), (0,16)

Answer 1

You can plot the three points on graph paper, calculate the slopes of the two segments that look like they may be perpendicular, them multiply the two slopes that were just calculated. If you get a -1 then the two segments are perpendicular and you have a right triangle.

Or you can just plot the three points in a free program like GeoGebra and use the software to calculate the angles.