Question

find the distance between the points (2, 2) and (4, 9). write your answer as a whole number or a fully simplified radical expression. do not round.

units

Explanation:

Step1: Recall the distance formula

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

Step2: Identify the coordinates

Here, \(x_1 = 2\), \(y_1 = 2\), \(x_2 = 4\), \(y_2 = 9\).

Step3: Substitute into the formula

First, calculate the differences: \(x_2 - x_1=4 - 2 = 2\) and \(y_2 - y_1=9 - 2 = 7\).
Then, square these differences: \((x_2 - x_1)^2=2^2 = 4\) and \((y_2 - y_1)^2=7^2 = 49\).
Next, add the squared differences: \(4 + 49 = 53\).
Finally, take the square root: \(d=\sqrt{53}\).

Answer:

\(\sqrt{53}\)