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Find the distance between the points $(6,0)$ and $(2,3)$ . $\newline$ 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

(6,0)

and

(2,3)

.

\newline

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

\newline

\_\_

units

Identify Coordinates: Identify the coordinates of the two points and the distance formula. $\newline$ The coordinates are given as $(6,0)$ for the first point and $(2,3)$ for the second point. The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ .
Substitute into Formula: Substitute the coordinates into the distance formula. $\newline$ Distance = $\sqrt{(2-6)^2 + (3-0)^2}$
Calculate Differences: Calculate the differences for each coordinate. $\newline$ Difference in $x$ -coordinates: $(2-6) = -4$ $\newline$ Difference in $y$ -coordinates: $(3-0) = 3$
Square Each Difference: Square each difference. $\newline$ Square of the difference in x-coordinates: $(-4)^2 = 16$ $\newline$ Square of the difference in y-coordinates: $(3)^2 = 9$
Add Squares: Add the squares of the differences. $\newline$ Sum of the squares: $16 + 9 = 25$
Take Square Root: Take the square root of the sum to find the distance. $\newline$ Distance = $\sqrt{25} = 5$

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