Pre-Calculus, 9th edition
111

 PAGE: 32 SET: Exercises PROBLEM: 111

Let the vertices of the triangle be  , , and .

Each two vertices form a line segment.

Find the slopes of three sides of the triangle.

The formula for slope is .

Find the slope of .

Substitute for , for , for   and for in .

.

Find the slope of .

Substitute for , for , for   and for in .

.

Find the slope of .

Substitute for , for , for   and for in .

.

Observe the three side slopes are , , and .

Perpendicular lines slopes are negative reciprocals to each other.

Therefore, the sides of the triangle and are perpendicular.

Perpendicular lines intersect at right angles to one another.

is a right angle triangle.

Thus, , , and are vertices of right triangle.

, , and are vertices of right triangle.

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