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Find the distance between the points $(6,8)$ and $(3,4)$ . $\newline$ $\newline$ 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

(6,8)

and

(3,4)

.

\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 formula to use. $\newline$ We have the points $(6,8)$ and $(3,4)$ . To find the distance between two points in a plane, we use the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ .
Plug Coordinates into Formula: Plug the coordinates into the distance formula. Using the points $(6,8)$ as $(x_1, y_1)$ and $(3,4)$ as $(x_2, y_2)$ , we get the distance as $\sqrt{(3-6)^2 + (4-8)^2}$ .
Calculate Differences and Square: Calculate the differences and square them. $\newline$ Calculate $(3-6)^2$ and $(4-8)^2$ . $\newline$ $(3-6)^2 = (-3)^2 = 9$ $\newline$ $(4-8)^2 = (-4)^2 = 16$
Add Squares and Find Square Root: Add the squares and find the square root. $\newline$ Now we add the squares of the differences: $\sqrt{9 + 16}$ . $\newline$ $\sqrt{9 + 16} = \sqrt{25} = 5$

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