Find the distance between the points (6,10) and (10,7). Write your answer as a whole number or a fully simplified radical expression. Do not round. ______ units

Distance Formula: To find the distance between two points, we use the distance formula: sqrt((x_2-x_1)^2 + (y_2-y_1)^2). For the points (6,10) and (10,7), we have (x_1, y_1) = (6, 10) and (x_2, y_2) = (10, 7).Calculate x-coordinate difference: Now we calculate the difference in the x-coordinates: (x_2-x_1) = (10-6) = 4.Calculate y-coordinate difference: Next, we calculate the difference in the y-coordinates: (y_2-y_1) = (7-10) = -3. Since we will be squaring this value, the negative sign will not affect the result.Square the differences: We now square the differences: (x_2-x_1)^2 = 4^2 = 16 and (y_2-y_1)^2 = (-3)^2 = 9.Add squared differences: We add the squared differences to find the distance: sqrt((x_2-x_1)^2 + (y_2-y_1)^2) = sqrt(16 + 9) = sqrt(25).Find the distance: Finally, we take the square root of 25 to get the distance: sqrt(25) = 5.

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Find the distance between the points $(6,10)$ and $(10,7)$ . $\newline$ Write your answer as a whole number or a fully simplified radical expression. Do not round. $\newline$ $\_\_$ units

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Algebra 1

Distance between two points

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Q. Find the distance between the points

(6,10)

and

(10,7)

\newline

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

\newline

\_\_

units

Distance Formula: To find the distance between two points, we use the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(6,10)$ and $(10,7)$ , we have $(x_1, y_1) = (6, 10)$ and $(x_2, y_2) = (10, 7)$ .
Calculate x-coordinate difference: Now we calculate the difference in the x-coordinates: $(x_2-x_1) = (10-6) = 4$ .
Calculate y-coordinate difference: Next, we calculate the difference in the y-coordinates: $(y_2-y_1) = (7-10) = -3$ . Since we will be squaring this value, the negative sign will not affect the result.
Square the differences: We now square the differences: $(x_2-x_1)^2 = 4^2 = 16$ and $(y_2-y_1)^2 = (-3)^2 = 9$ .
Add squared differences: We add the squared differences to find the distance: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} = \sqrt{16 + 9} = \sqrt{25}$ .
Find the distance: Finally, we take the square root of $25$ to get the distance: $\sqrt{25} = 5$ .