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Find the distance between the points $(10,8)$ and $(6,5)$ . $\newline$ $\newline$ 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

(10,8)

and

(6,5)

.

\newline

\newline

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

\newline

\newline

\_\_

units

Identify Coordinates and Formula: Identify the coordinates of the two points and the distance formula. $\newline$ The coordinates are given as $(10,8)$ for the first point and $(6,5)$ 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 coordinates $(10,8)$ and $(6,5)$ , we get the following expression for the distance: $\newline$ Distance: $\sqrt{(6-10)^2 + (5-8)^2}$
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ For the $x$ -coordinates: $(6-10) = -4$ $\newline$ For the $y$ -coordinates: $(5-8) = -3$
Square Coordinate Differences: Square the differences. $\newline$ Squaring the x-coordinate difference: $(-4)^2 = 16$ $\newline$ Squaring the y-coordinate difference: $(-3)^2 = 9$
Add Squared Differences: Add the squared differences. $\newline$ Adding the squared differences: $16 + 9 = 25$
Find Distance: Take the square root of the sum to find the distance. $\newline$ The square root of $25$ is $5$ , so the distance is $\sqrt{25}$ which equals $5$ .

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