Question

question 1 of 5
what is the distance, in coordinate units, between the points (12,12) and (10,13) in the standard (x,y) coordinate plane?
√5
√6
3
5

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(12,12)\) and \((x_2,y_2)=(10,13)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(10 - 12)^2+(13 - 12)^2}\)

Step3: Calculate the differences

\(10-12=-2\) and \(13 - 12 = 1\)
So \(d=\sqrt{(-2)^2+1^2}\)

Step4: Square the differences

\((-2)^2=4\) and \(1^2 = 1\)
Then \(d=\sqrt{4 + 1}\)

Step5: Sum and take the square - root

\(4+1=5\), so \(d=\sqrt{5}\)

Answer:

\(\sqrt{5}\)