Question

7 essay 0 points what process would you use to find the distance between (2,7) and (4,10)? edit view insert format tools table 12pt paragraph b i u a t 4

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(2,7)\) and \((x_2,y_2)=(4,10)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(4 - 2)^2+(10 - 7)^2}\)

Step3: Calculate the differences

\(x_2 - x_1=4 - 2 = 2\), \(y_2 - y_1=10 - 7 = 3\)

Step4: Square the differences

\((x_2 - x_1)^2=2^2 = 4\), \((y_2 - y_1)^2=3^2 = 9\)

Step5: Sum the squares

\((x_2 - x_1)^2+(y_2 - y_1)^2=4 + 9=13\)

Step6: Take the square root

\(d=\sqrt{13}\)

Answer:

First, identify the coordinates \((x_1,y_1)=(2,7)\) and \((x_2,y_2)=(4,10)\). Then use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Substitute the values: \(d=\sqrt{(4 - 2)^2+(10 - 7)^2}\). Calculate the differences: \(x_2 - x_1 = 2\), \(y_2 - y_1=3\). Square the differences: \((x_2 - x_1)^2 = 4\), \((y_2 - y_1)^2=9\). Sum the squares: \(4 + 9 = 13\). Finally, take the square root: \(d=\sqrt{13}\). So the distance between the two points \((2,7)\) and \((4,10)\) is \(\sqrt{13}\)