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Find the distance between the points $(7,7)$ and $(3,10)$ . $\newline$ $\newline$ 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

(7,7)

and

(3,10)

.

\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 $(7,7)$ and $(3,10)$ , we have $(x_1, y_1) = (7, 7)$ and $(x_2, y_2) = (3, 10)$ . $\newline$ Distance: $\sqrt{(3-7)^2 + (10-7)^2}$
Calculate X-coordinate Difference: Calculate the difference in the x-coordinates and square it. $\newline$ What is $(3-7)^2$ ? $\newline$ $(3-7)^2$ $\newline$ = $(-4)^2$ $\newline$ = $16$
Calculate Y-coordinate Difference: Calculate the difference in the y-coordinates and square it. $\newline$ What is $(10-7)^2$ ? $\newline$ $(10-7)^2$ $\newline$ = $(3)^2$ $\newline$ = $9$
Add Squares and Find Square Root: Add the squares of the differences and find the square root. $\newline$ What is $\sqrt{16 + 9}$ ? $\newline$ $\sqrt{16 + 9}$ $\newline$ = $\sqrt{25}$ $\newline$ = $5$

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