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Find the distance between the points $(2,10)$ and $(5,6)$ . $\newline$ $\newline$ 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

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Q. Find the distance between the points

(2,10)

and

(5,6)

.

\newline

\newline

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

\newline

\newline

______ units

Distance Formula: To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ , we use the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(2,10)$ and $(5,6)$ , we have $(x_1, y_1) = (2, 10)$ and $(x_2, y_2) = (5, 6)$ .
Calculate x-coordinate difference: First, we calculate the difference in the x-coordinates: \(5 - $2$ )^ $2$ \. \(5 - $2$ )^ $2$ = ( $3$ )^ $2$ = $9$ \
Calculate y-coordinate difference: Next, we calculate the difference in the y-coordinates: $(6 - 10)^2$ . $(6 - 10)^2 = (-4)^2 = 16$ .
Add squared differences: Now, we add the squares of the differences in the $x$ and $y$ coordinates: $9 + 16$ . $\newline$ $9 + 16 = 25$ .
Find the distance: Finally, we take the square root of the sum to find the distance: $\sqrt{25}$ . $\newline$ $\sqrt{25} = 5$ .

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