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Find the distance between the points $(3,1)$ and $(9,9)$ . Write your answer as a whole number or a fully simplified radical expression. Do not round.

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Distance formula

Full solution

Q. Find the distance between the points

(3,1)

and

(9,9)

. Write your answer as a whole number or a fully simplified radical expression. Do not round.

Identify Coordinates: Identify the coordinates of the two points. $\newline$ We have Point A $(3, 1)$ and Point B $(9, 9)$ . From these points, we can determine the values of $x_1$ , $y_1$ , $x_2$ , and $y_2$ . $\newline$ $x_1 = 3$ , $y_1 = 1$ , $x_2 = 9$ , $y_2 = 9$ .
Apply Distance Formula: Apply the distance formula. $\newline$ The distance formula is $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ . We will substitute the values of $x_1$ , $y_1$ , $x_2$ , and $y_2$ into this formula. $\newline$ $d = \sqrt{(9 - 3)^2 + (9 - 1)^2}$ .
Calculate Differences: Calculate the differences and square them. $\newline$ Calculate $(9 - 3)^2$ and $(9 - 1)^2$ . $\newline$ $(9 - 3)^2 = 6^2 = 36$ , $\newline$ $(9 - 1)^2 = 8^2 = 64$ .
Add Squares: Add the squares together. $\newline$ Add $36$ and $64$ to get the sum under the square root. $\newline$ $36 + 64 = 100$ .
Take Square Root: Take the square root of the sum to find the distance. $\newline$ $d = \sqrt{100}$ . $\newline$ Since the square root of $100$ is $10$ , the distance $d$ is $10$ . $\newline$ $d = 10$ units.

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