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Find the distance between the points $(2,4)$ and $(6,7)$ . $\newline$ $\newline$ 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

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Q. Find the distance between the points

(2,4)

and

(6,7)

.

\newline

\newline

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

\newline

\newline

______ units

Introduction: To find the distance between two points in a coordinate plane, we use the distance formula, which is derived from the Pythagorean theorem. The distance formula is: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(2,4)$ and $(6,7)$ , we have $(x_1, y_1) = (2, 4)$ and $(x_2, y_2) = (6, 7)$ . Let's calculate the differences $(x_2-x_1)$ and $(y_2-y_1)$ first.
Calculate x-coordinate difference: Calculate $(x_2-x_1)^2$ : $(6-2)^2$ = $(4)^2$ = $16$ This is the square of the difference in the x-coordinates.
Calculate y-coordinate difference: Calculate $(y_2-y_1)^2$ : $(7-4)^2$ = $(3)^2$ = $9$ This is the square of the difference in the y-coordinates.
Calculate distance: Now, we add the squares of the differences to find the distance: $\sqrt{16 + 9}$ $\newline$ = $\sqrt{25}$ $\newline$ = $5$ $\newline$ The distance between the points $(2,4)$ and $(6,7)$ is $5$ units.

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