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Find the distance between the points $(5,5)$ and $(9,8)$ . $\newline$ $\newline$ 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

(5,5)

and

(9,8)

.

\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. $\newline$ The coordinates are given as $(5,5)$ for the first point and $(9,8)$ for the second point. The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ .
Substitute into Distance Formula: Substitute the coordinates into the distance formula. Using the coordinates $(5,5)$ and $(9,8)$ , we get the following expression for the distance: $\sqrt{(9-5)^2 + (8-5)^2}$ .
Calculate X-coordinate Difference: Calculate the difference between the x-coordinates and square it. $\newline$ Calculate $(9-5)^2$ : $\newline$ $(9-5)^2 = (4)^2 = 16$ .
Calculate Y-coordinate Difference: Calculate the difference between the y-coordinates and square it. $\newline$ Calculate $(8-5)^2$ : $\newline$ $(8-5)^2 = (3)^2 = 9$ .
Add Squares and Find Square Root: Add the squares of the differences and find the square root. $\newline$ Calculate $\sqrt{16 + 9}$ : $\newline$ $\sqrt{16 + 9} = \sqrt{25} = 5$ .

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