Question

what is the distance, in coordinate units, between the points (-10,2) and (2,7) in the standard (x,y) coordinate plane?
√13
2√5
11
13

Explanation:

Step1: Identify the coordinates

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

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(x_2 - x_1=2-(-10)=12\), \(y_2 - y_1=7 - 2 = 5\)
Then \(d=\sqrt{12^{2}+5^{2}}=\sqrt{144 + 25}=\sqrt{169}\)

Step3: Simplify the square - root

\(\sqrt{169}=13\)

Answer:

13