Question

find the distance between the two points in simplest radical form. answer attempt 1 out of 2

Explanation:

1. First, assume the two - point formula:

• The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let's assume the two points from the graph are \((x_1,y_1)=(-7,-3)\) and \((x_2,y_2)=(2,1)\).

1. Then, calculate the differences in \(x\) and \(y\) coordinates:

• Calculate \(x_2 - x_1\): \(x_2 - x_1=2-(-7)=2 + 7 = 9\).
• Calculate \(y_2 - y_1\): \(y_2 - y_1=1-(-3)=1 + 3 = 4\).

1. Next, substitute into the distance formula:

• Substitute \(x_2 - x_1 = 9\) and \(y_2 - y_1 = 4\) into the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), we get \(d=\sqrt{9^2+4^2}\).
• Calculate \(9^2+4^2\): \(9^2 = 81\) and \(4^2 = 16\), so \(9^2+4^2=81 + 16=97\).
• Then \(d=\sqrt{97}\).

Step1: Identify the points

Let the points be \((-7,-3)\) and \((2,1)\)

Step2: Calculate \(x - \)coordinate difference

\(x_2 - x_1=2-(-7)=9\)

Step3: Calculate \(y - \)coordinate difference

\(y_2 - y_1=1-(-3)=4\)

Step4: Apply distance formula

\(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{9^2 + 4^2}\)

Step5: Simplify

\(d=\sqrt{81+16}=\sqrt{97}\)

Answer:

\(\sqrt{97}\)