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

(0,0)

and

(8,6)

.

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

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