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Find the distance between the points $(3,7)$ and $(7,10)$ . $\newline$ $\newline$ 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

(3,7)

and

(7,10)

.

\newline

\newline

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

\newline

\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 $(3,7)$ and $(7,10)$ , we have $(x_1, y_1) = (3, 7)$ and $(x_2, y_2) = (7, 10)$ . Let's calculate the distance using this formula.
Calculate X-coordinate Difference: First, we calculate the difference in the x-coordinates: $(x_2 - x_1) = (7 - 3)$ . This gives us $4$ . Now we square this difference: $(4)^2 = 16$ .
Calculate Y-coordinate Difference: Next, we calculate the difference in the y-coordinates: $(y_2 - y_1) = (10 - 7)$ . This gives us $3$ . Now we square this difference: $(3)^2 = 9$ .
Add Squares of Differences: We now add the squares of the differences in the $x$ and $y$ coordinates: $16 + 9 = 25$ .
Find Distance: Finally, we take the square root of the sum to find the distance: $\sqrt{25} = 5$ . Therefore, the distance between the points $(3,7)$ and $(7,10)$ is $5$ units.

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