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Find the distance between the points $(2,1)$ and $(5,5)$ . $\newline$ $\newline$ Write your answer as a whole number or a fully simplified radical expression. Do not round. $\newline$ $\newline$ $\_\_$ units

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Distance between two points

Full solution

Q. Find the distance between the points

(2,1)

and

(5,5)

.

\newline

\newline

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

\newline

\newline

\_\_

units

Identify Coordinates: Identify the coordinates of the two points and apply the distance formula. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(2,1)$ and $(5,5)$ , we have $(x_1, y_1) = (2, 1)$ and $(x_2, y_2) = (5, 5)$ .
Calculate Differences: Calculate the differences in the $x$ -coordinates and $y$ -coordinates. $\newline$ Difference in $x$ -coordinates: $(5-2)^2$ $\newline$ Difference in $y$ -coordinates: $(5-1)^2$
Square Differences: Square the differences. $\newline$ $(5-2)^2 = (3)^2 = 9$ $\newline$ $(5-1)^2 = (4)^2 = 16$
Find Distance: Add the squared differences and take the square root to find the distance. $\newline$ $\sqrt{9 + 16}$ $\newline$ $\sqrt{25}$ $\newline$ $= 5$

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