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Find the distance between the points $(2,7)$ and $(5,3)$ . Write your answer as a whole number or a fully simplified radical expression. Do not round.

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Distance formula

Full solution

Q. Find the distance between the points

(2,7)

and

(5,3)

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

Given Points: We have: $\newline$ Points: $(2, 7)$ and $(5, 3)$ $\newline$ Find the values of $x_1$ , $x_2$ , $y_1$ , and $y_2$ from the given points. $\newline$ $x_1 = 2$ $\newline$ $y_1 = 7$ $\newline$ $x_2 = 5$ $\newline$ $y_2 = 3$
Distance Formula: We know: $\newline$ Distance formula: $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ $\newline$ $x_1 = 2$ , $y_1 = 7$ , $x_2 = 5$ , and $y_2 = 3$ $\newline$ Substitute the values of $x_1$ , $y_1$ , $x_2$ , $y_2$ in the distance formula. $\newline$ $d = \sqrt{(5-2)^2 + (3-7)^2}$
Simplify Calculation: Simplify $(5-2)^2 + (3-7)^2$ . $\newline$ $(5-2)^2 + (3-7)^2$ $\newline$ = $3^2 + (-4)^2$ $\newline$ = $9 + 16$ $\newline$ = $25$
Find Distance: We have: $\newline$ $d = \sqrt{25}$ $\newline$ Find the distance between the points $(2,7)$ and $(5,3)$ . $\newline$ $\sqrt{25} = 5$ $\newline$ Distance between the points $(2,7)$ and $(5,3)$ is $5$ units.

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