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Find the distance between the points $(5,7)$ and $(1,4)$ . $\newline$ $\newline$ 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

(5,7)

and

(1,4)

.

\newline

\newline

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

\newline

\newline

\_\_

units

Identify Coordinates and Formula: Identify the coordinates of the two points and the distance formula. $\newline$ The coordinates are given as $(5,7)$ for the first point and $(1,4)$ for the second point. The distance formula is $\sqrt{((x_2-x_1)^2 + (y_2-y_1)^2)}$ .
Substitute into Formula: Substitute the coordinates into the distance formula. $\newline$ Distance: $\sqrt{(1-5)^2 + (4-7)^2}$
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ Difference in $x$ -coordinates: $(1-5) = -4$ $\newline$ Difference in $y$ -coordinates: $(4-7) = -3$
Square Coordinate Differences: Square the differences. $\newline$ Square of the difference in x-coordinates: $(-4)^2 = 16$ $\newline$ Square of the difference in y-coordinates: $(-3)^2 = 9$
Add Squares of Differences: Add the squares of the differences. $\newline$ Sum of the squares: $16 + 9 = 25$
Find Distance: Take the square root of the sum to find the distance. $\newline$ Distance: $\sqrt{25} = 5$

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