Question

what is the distance in the standard (x,y) coordinate plane between the points (-5, 0) and (0, 12)?
2√7
3√5
13
17

Explanation:

Step1: Recall 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, \(x_1=-5,y_1 = 0,x_2=0,y_2=12\).

Step2: Substitute the values into the formula

Substitute the values: \(d=\sqrt{(0-(-5))^2+(12 - 0)^2}=\sqrt{(5)^2+(12)^2}\).

Step3: Calculate the squares and sum

\(5^2 = 25\) and \(12^2=144\). Then \(25 + 144=169\).

Step4: Take the square - root

\(d=\sqrt{169}=13\).

Answer:

13