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Find the distance between the points $(9,5)$ and $(6,1)$ . $\newline$ $\newline$ 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

(9,5)

and

(6,1)

.

\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 $(9,5)$ for the first point and $(6,1)$ 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 $(9,5)$ and $(6,1)$ , we get the distance as $\sqrt{(6-9)^2 + (1-5)^2}$ .
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ For the $x$ -coordinates: $(6-9) = -3$ and $(-3)^2 = 9$ . $\newline$ For the $y$ -coordinates: $(1-5) = -4$ and $(-4)^2 = 16$ .
Find Square Root: Add the squares of the differences and find the square root. $\newline$ The sum of the squares is $9 + 16 = 25$ . The square root of $25$ is $\sqrt{25} = 5$ .

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