Question

Is the following shape a right triangle? How do you know?

Answer 1

Answer:

C.

Step-by-step explanation:

The only information you really need in order to determine if this is a right triangle are the slopes of segments AB and BC.  If the slopes of these segments are opposite reciprocals of one another, then the lines are perpendicular, and the angle is a right angle (making the triangle a right triangle!).  Point A has coordinates (-5, 5), B(-3, 2), C(-6, 0).

The slope of segment AB:

$m=\frac{2-5}{-3-(-5)}=-\frac{3}{2}$

The slope of segment BC:

$m=\frac{0-2}{-6-(-3)}=\frac{2}{3}$

As you can see, the slopes are opposite reciprocals of one another so angle ABC is a right angle, and triangle ABC is a right triangle.  Choice C is the one you want.