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Find the distance between the points $(1,3)$ and $(5,6)$ . $\newline$ $\newline$ 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

(1,3)

and

(5,6)

.

\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 formula to use. $\newline$ We have the points $(1,3)$ and $(5,6)$ . 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 $(1,3)$ and $(5,6)$ , we get: $\newline$ Distance $= \sqrt{(5 - 1)^2 + (6 - 3)^2}$
Calculate and Square Differences: Calculate the differences and square them. $\newline$ Calculate $(5 - 1)^2$ : $\newline$ $(5 - 1)^2 = 4^2 = 16$ $\newline$ Calculate $(6 - 3)^2$ : $\newline$ $(6 - 3)^2 = 3^2 = 9$
Add and Find Square Root: Add the squared differences and find the square root. $\newline$ Distance = $\sqrt{16 + 9}$ $\newline$ Distance = $\sqrt{25}$ $\newline$ Distance = $5$

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