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Find the distance between the points $(5,8)$ and $(9,5)$ . $\newline$ 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

(5,8)

and

(9,5)

.

\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 distance formula. $\newline$ The coordinates are given as $(5,8)$ for the first point and $(9,5)$ 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. $\newline$ Using the points $(5,8)$ and $(9,5)$ , we get the distance as $\sqrt{(9-5)^2 + (5-8)^2}$ .
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ For the $x$ -coordinates: $(9-5) = 4$ $\newline$ For the $y$ -coordinates: $(5-8) = -3$
Square Coordinate Differences: Square the differences. $\newline$ Squaring the x-coordinate difference: $(4)^2 = 16$ $\newline$ Squaring the y-coordinate difference: $(-3)^2 = 9$
Add Squares of Differences: Add the squares of the differences. $\newline$ Adding the results from Step $4$ : $16 + 9 = 25$
Find Square Root of Sum: Take the square root of the sum to find the distance. $\newline$ The square root of $25$ is $\sqrt{25} = 5$ .

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