Concept explainers
Show that the points , , and are the vertices of a right triangle in two ways:
(a) By using the converse of the Pythagorean Theorem
(b) By using the slopes of the lines joining the vertices
To show: The points are the vertices of a right triangle in two ways: (a) By using the converse of the Pythagorean Theorem (b) By using the slopes of the lines joining the vertices.
Answer to Problem 32RE
Explanation of Solution
If these three points are to make a right triangle, then that triangle must have a hypotenuse.
There are only three possibilities for the hypotenuse: the line , the line , or the line .
Here
Therefore the points are the vertices of a right triangle by Pythagorean Theorem.
(b) By using the slopes of the lines joining the vertices
Slope between and
Slope between and
Slope between and
Multiplication of slope between and is
Therefore the points are the vertices of a right triangle by using the slopes of the lines joining the vertices.
Chapter 1 Solutions
EBK PRECALC.:ENHANCED W/GRAPH.UTIL.
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