   Chapter 11.2, Problem 29E

Chapter
Section
Textbook Problem

# Classifying a TriangleIn Exercises 29–32, find the lengths of the sides of the triangle with the indicated vertices, and determine whether the triangle is a right triangle, an isosceles triangle, or neither. ( − 1 , 0 , − 2 ) , ( − 1 , 5 , 2 ) , ( − 3 , − 1 , 1 )

To determine

To calculate: The lengths of the sides of the triangle with vertices (1,0,2),(1, 5, 2),(3,1,1) and determine the type of triangle.

Explanation

Given:

The vertices are (1,0,2),(1, 5, 2),(3,1,1)

Formula used:

The distance formula is D= (x2x1)2+(y2y1)2+(z2z1)2

Calculation:

Consider the points represented as A=(1,0,2),B=(1, 5, 2),C=(3,1,1)

Now

AB = (1(1))2+(05)2+(22)2=02+(5)2 + (4)2=41

Then,

B</

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