Exercise 39 Page 322

To compare the side lengths of the triangle, we first need to graph the given vertices, A(2,4), B(-5,1), and C(0,0). Then we can connect the vertices with straight lines.

We will find the length of each of the sides using the Distance Formula. Let's start with finding the length of AB. The endpoints of AB are A( 2, 4) and B( -5, 1).

AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

SubstitutePoints

Substitute ( 2,4) & ( -5,1)

AB=sqrt(( -5- 2)^2+( 1- 4)^2)

▼

Calculate AB

SubTerms

Subtract terms

AB=sqrt((-7)^2+(-3)^2)

CalcPow

Calculate power

AB=sqrt(49+9)

AddTerms

Add terms

AB=sqrt(58)

CalcRoot

Calculate root

AB=7.61577310586...

RoundDec

Round to 1 decimal place(s)

AB ≈ 7.6

Let's repeat this procedure for other sides

Points	Distance Formula	Approximate Value
A( 2, 4) and B( -5, 1)	AB = sqrt(( -5- 2)^2+( 1- 4)^2)	7.6
B( -5, 1) and C( 0, 0)	BC = sqrt(( 0-( -5))^2+( 0- 1)^2)	5.1
C( 0, 0) and A( 2, 4)	CA=sqrt(( 2- 0)^2 + ( 4- 0)^2)	4.5

Knowing the lengths of each side, we can order them from shortest to longest. 4.5 < 5.1 < 7.6 ⇓ CA < BC < AB