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Find the distance between the points $(6,0)$ and $(0,8)$ . $\newline$ $\newline$ 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

(6,0)

and

(0,8)

.

\newline

\newline

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

\newline

\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 $(6,0)$ and $(0,8)$ , we have $(x_1, y_1) = (6, 0)$ and $(x_2, y_2) = (0, 8)$ . $\newline$ Distance: $\sqrt{(0-6)^2 + (8-0)^2}$
Calculate X-coordinate Difference: Calculate the difference in the x-coordinates and square it. $\newline$ What is $(0-6)^2$ ? $\newline$ $(0-6)^2$ $\newline$ = $(-6)^2$ $\newline$ = $36$
Calculate Y-coordinate Difference: Calculate the difference in the y-coordinates and square it. $\newline$ What is $(8-0)^2$ ? $\newline$ $(8-0)^2$ $\newline$ = $(8)^2$ $\newline$ = $64$
Add Squares and Find Square Root: Add the squares of the differences and find the square root. $\newline$ What is $\sqrt{36 + 64}$ ? $\newline$ $\sqrt{36 + 64}$ $\newline$ = $\sqrt{100}$ $\newline$ = $10$

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