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Find the distance between the points $(2,3)$ and $(6,6)$ . $\newline$ $\newline$ 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

(2,3)

and

(6,6)

.

\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 $(2,3)$ and $(6,6)$ . The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ .
Substitute into Formula: Substitute the coordinates into the distance formula. $\newline$ Using the points $(2,3)$ and $(6,6)$ , we get $\sqrt{(6-2)^2 + (6-3)^2}$ .
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ For the $x$ -coordinates: $(6-2) = 4$ . $\newline$ For the $y$ -coordinates: $(6-3) = 3$ .
Square the 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 results from Step $4$ : $16 + 9 = 25$ .
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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