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Find the distance between the points $(4,3)$ and $(1,7)$ . $\newline$ 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

(4,3)

and

(1,7)

.

\newline

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

\newline

\_\_

units

Identify Coordinates and Formula: Identify the coordinates of the two points and the formula to use. $\newline$ We have the points $(4,3)$ and $(1,7)$ . The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula: $\newline$ Distance = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Substitute into Distance Formula: Substitute the coordinates into the distance formula. $\newline$ Using the points $(4,3)$ and $(1,7)$ , we get: $\newline$ Distance = $\sqrt{(1 - 4)^2 + (7 - 3)^2}$
Calculate Squares of Differences: Calculate the squares of the differences. $\newline$ Calculate $(1 - 4)^2$ and $(7 - 3)^2$ : $\newline$ $(1 - 4)^2 = (-3)^2 = 9$ $\newline$ $(7 - 3)^2 = 4^2 = 16$
Add Squares of Differences: Add the squares of the differences. $\newline$ Add $9$ and $16$ to get the value under the square root: $\newline$ $\sqrt{9 + 16} = \sqrt{25}$
Calculate Square Root: Calculate the square root to find the distance. $\newline$ $\sqrt{25} = 5$ $\newline$ So, the distance between the points $(4,3)$ and $(1,7)$ is $5$ units.

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