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

(7,3)

and

(10,7)

.

\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 $(7,3)$ for the first point and $(10,7)$ 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 distance formula, we get $\sqrt{(10-7)^2 + (7-3)^2}$ .
Calculate X-coordinate Difference: Calculate the difference between the x-coordinates and square it. $\newline$ Calculate $(10-7)^2$ which is $3^2$ and equals $9$ .
Calculate Y-coordinate Difference: Calculate the difference between the y-coordinates and square it. $\newline$ Calculate $(7-3)^2$ which is $4^2$ and equals $16$ .
Add and Find Square Root: Add the squares of the differences and find the square root. $\newline$ Add $9 + 16$ to get $25$ and then find the square root of $25$ , which is $\sqrt{25} = 5$ .

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