Find the lengths of the sides of the right triangle whose vertices are located at the given points. Show that these lengths satisfy the Pythagorean Theorem. Show all of your work.
$$( - 6 , - 3,4 ) , ( - 7 , - 1,3 ) , ( 6,4,0 )$$

Question

Quizplus · Accepted Answer

The Answer is Let point

P = ( - 6 , - 3,4 )

, point

Q = ( - 7 , - 1,3 )

, and point

R = ( 6,4,0 )

.

\begin{array} { l } | \overline { P Q } | ^ { 2 } = ( - 7 + 6 ) ^ { 2 } + ( - 1 + 3 ) ^ { 2 } + ( 3 - 4 ) ^ { 2 } = 6 ; \Rightarrow | \overline { P Q } | = \sqrt { 6 } \| \overline { Q R } | ^ { 2 } = ( 6 + 7 ) ^ { 2 } + ( 4 + 1 ) ^ { 2 } + ( 0 - 3 ) ^ { 2 } = 203 ; \Rightarrow | \overline { Q R } | = \sqrt { 203 } \| \overline { P R } | ^ { 2 } = ( 6 + 6 ) ^ { 2 } + ( 4 + 3 ) ^ { 2 } + ( 0 - 4 ) ^ { 2 } = 209 ; \Rightarrow | \overline { P R } | = \sqrt { 209 }\end{array}

Note that

6 + 203 = 209

in accordance with the Pythagorean Theorem.

Find the Lengths of the Sides of the Right Triangle (−6,−3,4),(−7,−1,3),(6,4,0)( - 6 , - 3,4 ) , ( - 7 , - 1,3 ) , ( 6,4,0 )(−6,−3,4),(−7,−1,3),(6,4,0)

Find the Lengths of the Sides of the Right Triangle $( - 6 , - 3,4 ) , ( - 7 , - 1,3 ) , ( 6,4,0 )$