Exercise 5 Page 718

We want to find the length of each line segment with the given endpoints. Then we will order the segments from shortest to longest.

Endpoints
A(1,- 5)	B(4,0)
C(- 4,2)	D(1,4)
E(- 1,1)	F(- 2,7)
G(- 1.5,0)	H(4.5,0)
J(-7, - 8)	K(- 3,- 5)
L(10,- 2)	M(9,6)

The length of a segment is the distance d between its endpoints (x_1, y_1) and (x_2,y_2). We can use the Distance Formula to find the lengths of each of the line segments. Let's recall the Distance Formula. d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2) We will start with the first segment. The endpoints are A( 1, - 5) and B( 4, 0). Let's substitute these coordinates into the formula and evaluate. The length of AB is approximately 5.83 units. Following similar steps, we will find the lengths of the remaining segments.

Endpoints		Substitute	Evaluate
A( 1, - 5)	B( 4, 0)	sqrt(( 4- 1)^2+( 0-( - 5))^2)	≈ 5.83
C( - 4, 2)	D( 1, 4)	sqrt(( 1-( - 4))^2+( 4- 2)^2)	≈ 5.39
E( - 1, 1)	F( - 2, 7)	sqrt(( - 2-( - 1))^2+( 7- 1)^2)	≈ 6.08
G( - 1.5, 0)	H( 4.5, 0)	sqrt(( 4.5-( - 1.5))^2+( 0- 0)^2)	6
J( - 7, - 8)	K( - 3, - 5)	sqrt(( - 3-( - 7))^2+( - 5-( - 8))^2)	5
L( 10, - 2)	M( 9, 6)	sqrt(( 9- 10)^2+( 6-( - 2))^2)	≈ 8.06

We can now order the segments from shortest to longest, where 1 is the shortest segment and 6 is the longest.

Endpoints		Length	Order
A(1,- 5)	B(4,0)	≈ 5.83	3
C(- 4,2)	D(1,4)	≈ 5.39	2
E(- 1,1)	F(- 2,7)	≈ 6.08	5
G(- 1.5,0)	H(4.5,0)	6	4
J(-7, - 8)	K(- 3,- 5)	5	1
L(10,- 2)	M(9,6)	≈ 8.06	6