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Find the distance between the points $(6,3)$ and $(9,7)$ . $\newline$ $\newline$ 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

(6,3)

and

(9,7)

.

\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 distance formula. $\newline$ The coordinates are given as $(6,3)$ for the first point and $(9,7)$ for the second point. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ .
Plug into Distance Formula: Plug the coordinates into the distance formula. $\newline$ Using the distance formula, we substitute $(x_1 , y_1) = (6 , 3)$ and $(x_2 , y_2) = (9 , 7)$ . $\newline$ Distance: $\sqrt{(9-6)^2 + (7-3)^2}$
Calculate X-coordinate Difference: Calculate the difference between the x-coordinates and square it. $\newline$ What is $(9-6)^2$ ? $\newline$ $(9-6)^2$ $\newline$ = $(3)^2$ $\newline$ = $9$
Calculate Y-coordinate Difference: Calculate the difference between the y-coordinates and square it. $\newline$ What is $(7-3)^2$ ? $\newline$ $(7-3)^2$ $\newline$ = $(4)^2$ $\newline$ = $16$
Add Squares and Find Square Root: Add the squares of the differences and find the square root. $\newline$ What is $\sqrt{9 + 16}$ ? $\newline$ $\sqrt{9 + 16}$ $\newline$ = $\sqrt{25}$ $\newline$ = $5$

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