Find the distance between the points (4,2) and (10,10). Write your answer as a whole number or a fully simplified radical expression. Do not round. ______ units

Apply Distance Formula: To find the distance between two points (x1, y1) and (x2, y2), we use the distance formula: sqrt((x2-x1)^2 + (y2-y1)^2). Let's apply this formula to the points (4,2) and (10,10).Calculate x-coordinate difference: First, calculate the difference in the x-coordinates: (10 - 4)^2. This equals 6^2, which is 36.Calculate y-coordinate difference: Next, calculate the difference in the y-coordinates: (10 - 2)^2. This equals 8^2, which is 64.Add squares of differences: Now, add the squares of the differences: 36 + 64. This equals 100.Find the distance: Finally, take the square root of the sum to find the distance: sqrt(100). The square root of 100 is 10.

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Find the distance between the points $(4,2)$ and $(10,10)$ . $\newline$ 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

(4,2)

and

(10,10)

\newline

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

\newline

______ units

Apply Distance Formula: To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ , we use the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . Let's apply this formula to the points $(4,2)$ and $(10,10)$ .
Calculate x-coordinate difference: First, calculate the difference in the x-coordinates: $(10 - 4)^2$ . This equals $6^2$ , which is $36$ .
Calculate y-coordinate difference: Next, calculate the difference in the y-coordinates: $(10 - 2)^2$ . This equals $8^2$ , which is $64$ .
Add squares of differences: Now, add the squares of the differences: $36 + 64$ . This equals $100$ .
Find the distance: Finally, take the square root of the sum to find the distance: $\sqrt{100}$ . The square root of $100$ is $10$ .