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Find the distance between the points $(8,1)$ and $(5,5)$ . $\newline$ $\newline$ 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

(8,1)

and

(5,5)

.

\newline

\newline

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

\newline

\newline

\_\_

units

Identify Coordinates: 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 $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . Let's apply this formula to the points $(8,1)$ and $(5,5)$ .
Substitute Values: First, we identify the coordinates of the two points. We have $(x_1, y_1) = (8, 1)$ and $(x_2, y_2) = (5, 5)$ . Now we substitute these values into the distance formula.
Calculate X-coordinate Difference: Calculate the difference in the x-coordinates: $(x_2 - x_1) = (5 - 8) = -3$ . Squaring this difference gives us $(-3)^2 = 9$ .
Calculate Y-coordinate Difference: Calculate the difference in the y-coordinates: $(y_2 - y_1) = (5 - 1) = 4$ . Squaring this difference gives us $(4)^2 = 16$ .
Add Squares and Find Distance: Now we add the squares of the differences in the $x$ and $y$ coordinates: $9 + 16 = 25$ .
Add Squares and Find Distance: Now we add the squares of the differences in the $x$ and $y$ coordinates: $9 + 16 = 25$ .Finally, we take the square root of the sum to find the distance: $\sqrt{25} = 5$ . This is the distance between the two points.

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