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Find the distance between the points $(4,5)$ and $(8,8)$ . $\newline$ Write your answer as a whole number or a fully simplified radical expression. Do not round. $\newline$ $\_\_$ units

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Distance between two points

Full solution

Q. Find the distance between the points

(4,5)

and

(8,8)

.

\newline

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

\newline

\_\_

units

Distance Formula: To find the distance between two points in a coordinate plane, we use the distance formula, which is derived from the Pythagorean theorem. The distance formula is: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(4,5)$ and $(8,8)$ , we have $(x_1, y_1) = (4, 5)$ and $(x_2, y_2) = (8, 8)$ . Let's plug these values into the distance formula.
Calculate x-coordinate difference: First, we calculate the difference in the x-coordinates: $(x_2-x_1) = (8-4)$ . This gives us $4$ .
Calculate y-coordinate difference: Next, we calculate the difference in the y-coordinates: $(y_2-y_1) = (8-5)$ . This gives us $3$ .
Square differences: Now we square both differences: $(x_2-x_1)^2 = 4^2 = 16$ and $(y_2-y_1)^2 = 3^2 = 9$ .
Add squared differences: We then add these squared differences together: $16 + 9 = 25$ .
Find distance: Finally, we take the square root of the sum to find the distance: $\sqrt{25} = 5$ . This is the distance between the points $(4,5)$ and $(8,8)$ .

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