Question

find the length of the segment. round to two decimal places if necessary.

Explanation:

1. First, assume the two - endpoints of the line segment:

• Let's assume the endpoints of the line segment are \((x_1,y_1)\) and \((x_2,y_2)\). From the graph, if we assume one endpoint is \((- 4,-10)\) and the other is \((7,0)\).
• The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

1. Then, substitute the values of \(x_1,y_1,x_2,y_2\) into the formula:

• Here, \(x_1=-4,y_1 = - 10,x_2 = 7,y_2 = 0\).
• First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
• \(x_2 - x_1=7-(-4)=7 + 4=11\).
• \(y_2 - y_1=0-(-10)=0 + 10 = 10\).
• Then, calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\):
• \((x_2 - x_1)^2+(y_2 - y_1)^2=11^2+10^2=121 + 100=221\).
• Finally, calculate the distance \(d\):
• \(d=\sqrt{221}\approx14.87\).

Step1: Identify endpoints

Assume endpoints \((-4,-10)\) and \((7,0)\)

Step2: Apply distance formula

\(d=\sqrt{(7-(-4))^2+(0 - (-10))^2}=\sqrt{(7 + 4)^2+(0 + 10)^2}=\sqrt{11^2+10^2}\)

Step3: Calculate squares and sum

\(11^2+10^2=121 + 100 = 221\), so \(d=\sqrt{221}\)

Step4: Round result

\(d\approx14.87\)

Answer:

\(14.87\)