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Chapter 1: Q. 102 (page 16)

In Problems 101鈥�104, find the length of each side of the triangle determined by the three points P1 , P2 , and P3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.)

P1=-1,4,P2=6,2,P3=4,-5

Short Answer

Expert verified

The length of sides of triangle are 53,53and106.

The triangle is a Right Triangle.

Step by step solution

01

. Given Information

The coordinate of vertex of triangle are as follows

P1=-1,4,P2=6,2,P3=4,-5
02

Step 2. Distance betweenP1 and P2

dP1,P2=-1-62+4-22=49+4=53

03

Step 3. Distance between P2 and P3

dP2,P3=4-62+-5-22=4+49=53

04

Step 4. Distance between P1 and P3

dP1,P3=-1-42+4+52=25+81=106

05

Step 5. Check for Right Triangle

532+532=106253+53=106

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