Question

what is the distance between $(-13,9)$ and $(11,2)$ on a coordinate grid?

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-13,9)\) and \((x_2,y_2)=(11,2)\).

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(x_2 - x_1=11-(-13)=11 + 13=24\), \(y_2 - y_1=2 - 9=-7\).
Then \(d=\sqrt{(24)^2+(-7)^2}=\sqrt{576 + 49}=\sqrt{625}\).

Step3: Calculate the square - root

Since \(\sqrt{625}=25\).

Answer:

\(25\)