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

Full solution

Q. Find the distance between the points

(5,2)

and

(2,6)

.

\newline

\newline

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

\newline

\newline

\_\_

units

Identify Points: To find the distance between two points, we use the distance formula, which is derived from the Pythagorean theorem. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(5,2)$ and $(2,6)$ , we have $(x_1, y_1) = (5, 2)$ and $(x_2, y_2) = (2, 6)$ .
Calculate x-coordinate Difference: First, we calculate the difference in the x-coordinates: $(x_2-x_1) = (2-5)$ .
Square x-coordinate Difference: Now, we square the difference in the x-coordinates: \(2 $-5$ )^ $2$ = ( $-3$ )^ $2$ = $9$ \
Calculate y-coordinate Difference: Next, we calculate the difference in the y-coordinates: $(y_2-y_1) = (6-2)$ .
Square y-coordinate Difference: Then, we square the difference in the y-coordinates: $(6-2)^2 = (4)^2 = 16$ .
Add Squares of Differences: Now, we add the squares of the differences in the $x$ and $y$ coordinates: $9 + 16 = 25$ .
Find Distance: Finally, we take the square root of the sum to find the distance: $\sqrt{25} = 5$ .

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