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Find the distance between the points $(6,1)$ and $(2,4)$ . $\newline$ 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

(6,1)

and

(2,4)

.

\newline

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

\newline

\_\_\_\_\_\_

units

Use Distance Formula: We will use the distance formula to find the distance between the points $(6,1)$ and $(2,4)$ . The distance formula is $\sqrt{((x_2-x_1)^2 + (y_2-y_1)^2)}$ . Here, $(x_1 , y_1) = (6 , 1)$ and $(x_2 , y_2) = (2 , 4)$ .
Calculate X-coordinate Difference: First, we calculate the difference in the x-coordinates: $(x_2-x_1)^2 = (2-6)^2$ .
Square X-coordinate Difference: Calculating the square of the difference in x-coordinates: $(2-6)^2 = (-4)^2 = 16$ .
Calculate Y-coordinate Difference: Next, we calculate the difference in the y-coordinates: $(y_2-y_1)^2 = (4-1)^2$ .
Square Y-coordinate Difference: Calculating the square of the difference in y-coordinates: $(4-1)^2 = (3)^2 = 9$ .
Add Squares of Differences: Now, we add the squares of the differences in $x$ and $y$ -coordinates: $16 + 9 = 25$ .
Find Distance: Finally, we take the square root of the sum to find the distance: $\sqrt{25} = 5$ .

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