Question

find the length of the segment. round to the nearest tenth, if necessary. 11. 12.

Explanation:

1. For problem 11:

• Assume the two - endpoints of the line segment are \((x_1,y_1)\) and \((x_2,y_2)\). From the graph, if we assume the endpoints are \((- 4,-4)\) and \((3,0)\).

Step1: Identify the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Substitute the values

Here, \(x_1=-4,y_1 = - 4,x_2=3,y_2 = 0\). So \(d=\sqrt{(3-(-4))^2+(0 - (-4))^2}=\sqrt{(3 + 4)^2+(0 + 4)^2}=\sqrt{7^2+4^2}=\sqrt{49 + 16}=\sqrt{65}\approx8.1\).

1. For problem 12:

• Assume the two endpoints of the line segment are \((x_1,y_1)\) and \((x_2,y_2)\). From the graph, if we assume the endpoints are \((-2,1)\) and \((-2,5)\).

Step1: Identify the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Substitute the values

Here, \(x_1=-2,y_1 = 1,x_2=-2,y_2 = 5\). So \(d=\sqrt{(-2-(-2))^2+(5 - 1)^2}=\sqrt{(-2 + 2)^2+4^2}=\sqrt{0^2+4^2}=\sqrt{16}=4\).

Answer:

1. Approximately \(8.1\)
2. \(4\)