Find the distance between the points (10,10) and (6,7). Write your answer as a whole number or a fully simplified radical expression. Do not round. ______ units

Identify Coordinates and Formula: Identify the coordinates of the two points and the distance formula. The coordinates are given as (10,10) for the first point and (6,7) 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. Using the points (10,10) and (6,7), we get sqrt((6-10)^2 + (7-10)^2).Calculate Coordinate Differences: Calculate the differences for the x-coordinates and the y-coordinates. For the x-coordinates: (6-10) = -4 For the y-coordinates: (7-10) = -3Square the Differences: Square the differences. For the x-coordinates: (-4)^2 = 16 For the y-coordinates: (-3)^2 = 9Add Squared Differences: Add the squared differences. 16 + 9 = 25Find the Distance: Take the square root of the sum to find the distance. sqrt(25) = 5

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Find the distance between the points $(10,10)$ and $(6,7)$ . $\newline$ $\newline$ Write your answer as a whole number or a fully simplified radical expression. Do not round. $\newline$ $\newline$ $\_\_\_\_\_\_$ units

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Algebra 1

Distance between two points

Full solution

Q. Find the distance between the points

(10,10)

and

(6,7)

\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 $(10,10)$ for the first point and $(6,7)$ 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. $\newline$ Using the points $(10,10)$ and $(6,7)$ , we get $\sqrt{(6-10)^2 + (7-10)^2}$ .
Calculate Coordinate Differences: Calculate the differences for the $x$ -coordinates and the $y$ -coordinates. $\newline$ For the $x$ -coordinates: $(6-10) = -4$ $\newline$ For the $y$ -coordinates: $(7-10) = -3$
Square the Differences: Square the differences. $\newline$ For the x-coordinates: $(-4)^2 = 16$ $\newline$ For the y-coordinates: $(-3)^2 = 9$
Add Squared Differences: Add the squared differences. $16 + 9 = 25$
Find the Distance: Take the square root of the sum to find the distance. $\sqrt{25} = 5$