Question

find the distance between the points (6, 1) and (2, 2). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Recall distance formula

The distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Here, \(x_1 = 6\), \(y_1 = 1\), \(x_2 = 2\), \(y_2 = 2\).

Step2: Substitute values into formula

Substitute the values into the formula:
\(d=\sqrt{(2 - 6)^2+(2 - 1)^2}\)
First, calculate the differences: \(2-6=-4\) and \(2 - 1 = 1\).

Step3: Square the differences

Square the results: \((-4)^2=16\) and \(1^2 = 1\).

Step4: Sum the squares

Sum the squared values: \(16+1 = 17\).

Step5: Take the square root

Take the square root of the sum: \(d=\sqrt{17}\).

Answer:

\(\sqrt{17}\)