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Find the distance between the points $(5,6)$ and $(8,10)$ . $\newline$ Write your answer as a whole number or a fully simplified radical expression. Do not round. $\newline$ ______ units

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Distance between two points

Full solution

Q. Find the distance between the points

(5,6)

and

(8,10)

.

\newline

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

\newline

______ units

Identify Coordinates and Formula: Identify the coordinates of the two points and the distance formula. $\newline$ The coordinates are given as $(5,6)$ for the first point and $(8,10)$ for the second point. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ .
Plug into Distance Formula: Plug the coordinates into the distance formula. $\newline$ Using the points $(5,6)$ and $(8,10)$ , we get the distance as $\sqrt{(8-5)^2 + (10-6)^2}$ .
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ For the $x$ -coordinates: $(8-5) = 3$ $\newline$ For the $y$ -coordinates: $(10-6) = 4$
Square Coordinate Differences: Square the differences. $\newline$ Square of the x-coordinate difference: $(3)^2 = 9$ $\newline$ Square of the y-coordinate difference: $(4)^2 = 16$
Add Squares of Differences: Add the squares of the differences. $\newline$ Add the results from Step $4$ : $9 + 16 = 25$
Find Distance: Take the square root of the sum to find the distance. $\newline$ The square root of $25$ is $\sqrt{25}$ which equals $5$ .

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