Question

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

Explanation:

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

• Let's assume the left - hand end - point of the line segment is \((x_1,y_1)=(- 11,2)\) and the right - hand end - point is \((x_2,y_2)=(2,9)\) (by estimating the coordinates from the graph).

1. Then, use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\):

• Substitute \(x_1=-11\), \(y_1 = 2\), \(x_2 = 2\), and \(y_2=9\) into the formula.
• First, calculate \(x_2 - x_1\): \(x_2 - x_1=2-(-11)=2 + 11=13\).
• Second, calculate \(y_2 - y_1\): \(y_2 - y_1=9 - 2=7\).
• Then, calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\): \((x_2 - x_1)^2+(y_2 - y_1)^2=13^2+7^2=169 + 49=218\).
• Finally, find \(d\): \(d=\sqrt{218}\approx14.76\).

Step1: Identify endpoints

\((x_1,y_1)=(-11,2),(x_2,y_2)=(2,9)\)

Step2: Apply distance formula

\(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Step3: Calculate differences

\(x_2 - x_1=13,y_2 - y_1 = 7\)

Step4: Calculate sum of squares

\((x_2 - x_1)^2+(y_2 - y_1)^2=169 + 49=218\)

Step5: Find distance

\(d=\sqrt{218}\approx14.76\)

Answer:

\(14.76\)