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Find the distance between the points $(4,8)$ and $(7,4)$ . $\newline$ 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

(4,8)

and

(7,4)

.

\newline

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

\newline

______ units

Identify Coordinates and Formula: Identify the coordinates of the two points and the formula to use. $\newline$ We have the points $(4,8)$ and $(7,4)$ . The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula: $\newline$ Distance = $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Substitute into Distance Formula: Substitute the coordinates into the distance formula. $\newline$ Using the points $(4,8)$ and $(7,4)$ , we get: $\newline$ Distance $= \sqrt{(7 - 4)^2 + (4 - 8)^2}$
Calculate Differences and Square: Calculate the differences and square them. $\newline$ Calculate $(7 - 4)^2$ : $\newline$ $(7 - 4)^2 = (3)^2 = 9$ $\newline$ Calculate $(4 - 8)^2$ : $\newline$ $(4 - 8)^2 = (-4)^2 = 16$ $\newline$ So, the distance is: $\newline$ Distance = $\sqrt{9 + 16}$
Add and Find Square Root: Add the squares and find the square root. $\newline$ Add $9$ and $16$ to get $25$ , then find the square root: $\newline$ Distance $= \sqrt{25} = 5$ $\newline$ So, the distance between the points $(4,8)$ and $(7,4)$ is $5$ units.

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