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Find the distance between the points $(1,10)$ and $(5,7)$ . $\newline$ $\newline$ 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

(1,10)

and

(5,7)

.

\newline

\newline

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

\newline

\newline

\_\_

units

Distance Formula Explanation: 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 $(1,10)$ and $(5,7)$ , we have $(x_1, y_1) = (1, 10)$ and $(x_2, y_2) = (5, 7)$ .
Calculate X-coordinate Difference: First, we calculate the difference in the x-coordinates: $(5 - 1)^2$ . This gives us $(4)^2 = 16$ .
Calculate Y-coordinate Difference: Next, we calculate the difference in the y-coordinates: $(7 - 10)^2$ . This gives us $(-3)^2 = 9$ .
Add Squares of Differences: Now, we add the squares of the differences in the $x$ and $y$ coordinates to find the distance: $\sqrt{16 + 9}$ . $\newline$ This simplifies to $\sqrt{25}$ .
Final Distance Calculation: Finally, we take the square root of $25$ , which is $5$ . Therefore, the distance between the points $(1,10)$ and $(5,7)$ is $5$ units.

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