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Find the distance between the points $(7,1)$ and $(1,9)$ . $\newline$ $\newline$ 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

(7,1)

and

(1,9)

.

\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 distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . $\newline$ Here, we have $(x_1, y_1) = (7, 1)$ and $(x_2, y_2) = (1, 9)$ .
Substitute into Distance Formula: Substitute the coordinates into the distance formula. $\newline$ Distance = $\sqrt{(1-7)^2 + (9-1)^2}$
Calculate Squares of Differences: Calculate the squares of the differences. $\newline$ Calculate $(1-7)^2$ and $(9-1)^2$ . $\newline$ $(1-7)^2 = (-6)^2 = 36$ $\newline$ $(9-1)^2 = (8)^2 = 64$
Add Squares of Differences: Add the squares of the differences. $\newline$ Add $36$ and $64$ . $\newline$ $36 + 64 = 100$
Find Distance: Take the square root of the sum to find the distance. $\newline$ Distance = $\sqrt{100}$ $\newline$ Distance = $10$

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