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Find the distance between the points $(1,5)$ and $(5,2)$ . $\newline$ $\newline$ 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

(1,5)

and

(5,2)

.

\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 formula to use. $\newline$ We have the points $(1,5)$ and $(5,2)$ . To find the distance between two points in a plane, we use the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ .
Substitute into Distance Formula: Substitute the coordinates into the distance formula. $\newline$ Using the points $(1,5)$ as $(x_1, y_1)$ and $(5,2)$ as $(x_2, y_2)$ , we get: $\newline$ Distance = $\sqrt{(5-1)^2 + (2-5)^2}$ .
Calculate and Square Differences: Calculate the differences and square them. $\newline$ Calculate $(5-1)^2$ : $\newline$ $(5-1)^2 = (4)^2 = 16$ . $\newline$ Calculate $(2-5)^2$ : $\newline$ $(2-5)^2 = (-3)^2 = 9$ .
Add and Find Square Root: Add the squares and find the square root. $\newline$ Add the results from Step $3$ : $\newline$ $16 + 9 = 25$ . $\newline$ Now, take the square root: $\newline$ $\sqrt{25} = 5$ .

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