Question

Consider AABC with vertices A B C (3,1), (1, 2),and (4, 2) as shown in the accompanying diagram.

Is the triangle a right triangle? Justfify.

Answer 1

yes; AB ⊥ BC

Explanation:

If the triangle is to be a right triangle, the slopes of two sides must be opposite reciprocals. The slope is the ratio of rise to run.

mAB = rise/run = -3/4

mBC = rise/run = 4/3

These slopes, -3/4 and 4/3 are opposite reciprocals (their product is -1), so ...

AB ⊥ BC . . . the triangle is a right triangle