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Find the distance between the points $(2,8)$ and $(8,0)$ . $\newline$ 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

(2,8)

and

(8,0)

.

\newline

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

\newline

______ units

Given Points: To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ , we use the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(2,8)$ and $(8,0)$ , we have $(x_1, y_1) = (2, 8)$ and $(x_2, y_2) = (8, 0)$ .
Calculate x Difference: First, we calculate the difference in the x-coordinates: $(x_2 - x_1) = (8 - 2) = 6$ .
Calculate y Difference: Next, we calculate the difference in the y-coordinates: $(y_2 - y_1) = (0 - 8) = -8$ . Since we are going to square this value, the negative sign will not affect the result.
Square Differences: Now, we square the differences: $(x_2 - x_1)^2 = 6^2 = 36$ and $(y_2 - y_1)^2 = (-8)^2 = 64$ .
Sum of Squares: We add the squared differences to find the sum under the square root: $36 + 64 = 100$ .
Find Distance: Finally, we take the square root of the sum to find the distance: $\sqrt{100} = 10$ .

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