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Find the distance between the points $(7,8)$ and $(10,4)$ . $\newline$ 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

(7,8)

and

(10,4)

.

\newline

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

\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 $(7,8)$ and $(10,4)$ , we have $(x_1, y_1) = (7, 8)$ and $(x_2, y_2) = (10, 4)$ .
Calculate X-Coordinate Difference: First, we calculate the difference in the x-coordinates: $(x_2 - x_1) = (10 - 7) = 3$ . Then we square this difference: $(3)^2 = 9$ .
Calculate Y-Coordinate Difference: Next, we calculate the difference in the y-coordinates: $(y_2 - y_1) = (4 - 8) = -4$ . Since we are going to square this difference, the negative sign will not affect the result: $(-4)^2 = 16$ .
Add Squares of Differences: Now, we add the squares of the differences in the $x$ and $y$ coordinates to find the square of the distance: $9 + 16 = 25$ .
Find Square Root: Finally, we take the square root of the sum to find the distance: $\sqrt{25} = 5$ . This is the distance between the points $(7,8)$ and $(10,4)$ .

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