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Find the distance between the points $(3,3)$ and $(7,0)$ . $\newline$ $\newline$ 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

(3,3)

and

(7,0)

.

\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 $(3,3)$ for the first point and $(7,0)$ for the second point. 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 $(3,3)$ and $(7,0)$ , we get the following expression for the distance: $\sqrt{(7-3)^2 + (0-3)^2}$ .
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ For the $x$ -coordinates: $(7-3) = 4$ . $\newline$ For the $y$ -coordinates: $(0-3) = -3$ .
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 $4$ : $16 + 9 = 25$ .
Take Square Root: Take the square root of the sum to find the distance. $\newline$ Calculating the square root of $25$ : $\sqrt{25} = 5$ .

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