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Find the distance between the points $(0,4)$ and $(3,0)$ . $\newline$ 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

(0,4)

and

(3,0)

.

\newline

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

\newline

\_\_

units

Identify Coordinates and Apply Formula: Identify the coordinates of the two points and apply the distance formula. $\newline$ The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(0,4)$ and $(3,0)$ , we have $(x_1, y_1) = (0, 4)$ and $(x_2, y_2) = (3, 0)$ . $\newline$ Distance: $\sqrt{(3-0)^2 + (0-4)^2}$
Calculate X-coordinate Difference: Calculate the difference in the x-coordinates and square it. $\newline$ What is $(3-0)^2$ ? $\newline$ $(3-0)^2$ $\newline$ = $(3)^2$ $\newline$ = $9$
Calculate Y-coordinate Difference: Calculate the difference in the y-coordinates and square it. $\newline$ What is $(0-4)^2$ ? $\newline$ $(0-4)^2$ $\newline$ = $(-4)^2$ $\newline$ = $16$
Add Squares and Find Distance: Add the squares of the differences and take the square root to find the distance. $\newline$ What is $\sqrt{9 + 16}$ ? $\newline$ $\sqrt{9 + 16}$ $\newline$ = $\sqrt{25}$ $\newline$ = $5$

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