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Find the distance between the points $(0,5)$ and $(4,2)$ . $\newline$ $\newline$ 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

(0,5)

and

(4,2)

.

\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 $(0,5)$ and $(4,2)$ . The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ .
Substitute into Distance Formula: Substitute the coordinates into the distance formula. Using the points $(0,5)$ and $(4,2)$ , we get the distance as $\sqrt{(4-0)^2 + (2-5)^2}$ .
Calculate and Square Differences: Calculate the differences and square them. $\newline$ Calculate $(4-0)^2$ and $(2-5)^2$ . $\newline$ $(4-0)^2 = 4^2 = 16$ $\newline$ $(2-5)^2 = (-3)^2 = 9$
Add and Find Square Root: Add the squared differences and find the square root. $\newline$ Add $16$ and $9$ to get $25$ , then take the square root of $25$ . $\newline$ $\sqrt{16 + 9} = \sqrt{25} = 5$

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