Question

what is the distance between $(-6,2)$ and $(8,10)$ on a coordinate grid? $sqrt{60}$ $sqrt{260}$ $sqrt{162}$ $sqrt{68}$

Explanation:

Step1: Use the 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, \(x_1=-6,y_1 = 2,x_2=8,y_2 = 10\).

Step2: Calculate \(x_2 - x_1\) and \(y_2 - y_1\)

\(x_2 - x_1=8-(-6)=8 + 6=14\), \(y_2 - y_1=10 - 2=8\).

Step3: Substitute into the formula

\(d=\sqrt{(14)^2+(8)^2}=\sqrt{196 + 64}=\sqrt{260}\)

Answer:

\(\sqrt{260}\)