Question

find the distance between the two points (-7,1) and (1,3).

Explanation:

Step1: Recall distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(-7,1)\) and \((x_2,y_2)=(1,3)\).

Step2: Substitute values into formula

First, calculate \(x_2 - x_1 = 1-(-7)=8\) and \(y_2 - y_1 = 3 - 1 = 2\). Then, substitute into the formula: \(d=\sqrt{(8)^2+(2)^2}=\sqrt{64 + 4}=\sqrt{68}\).

Step3: Simplify the square root

\(\sqrt{68}=\sqrt{4\times17}=2\sqrt{17}\approx 8.246\) (if decimal form is needed, but exact form is \(2\sqrt{17}\)).

Answer:

The distance between the two points is \(2\sqrt{17}\) (or approximately \(8.25\)).