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Find the distance between the points $(3,6)$ and $(0,2)$ . $\newline$ $\newline$ 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

(3,6)

and

(0,2)

.

\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 $(3,6)$ for the first point and $(0,2)$ 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 $(3,6)$ and $(0,2)$ , we get the following expression for the distance: $\sqrt{(0-3)^2 + (2-6)^2}$ .
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ For the $x$ -coordinates: $(0-3) = -3$ , and for the $y$ -coordinates: $(2-6) = -4$ .
Square Coordinate Differences: Square the differences. $\newline$ Squaring $-3$ gives us $(-3)^2 = 9$ , and squaring $-4$ gives us $(-4)^2 = 16$ .
Add Squares of Differences: Add the squares of the differences. $\newline$ Adding the results from the previous step, we get $9 + 16 = 25$ .
Find Square Root of Sum: Take the square root of the sum to find the distance. $\newline$ The square root of $25$ is $\sqrt{25} = 5$ .

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