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Find the distance between the points $(9,9)$ and $(6,5)$ . $\newline$ $\newline$ 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

(9,9)

and

(6,5)

.

\newline

\newline

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

\newline

\newline

\_\_

units

Distance Formula: To find the distance between two points, we use the distance formula: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ . For the points $(9,9)$ and $(6,5)$ , we have $(x_1, y_1) = (9, 9)$ and $(x_2, y_2) = (6, 5)$ . $\newline$ Distance: $\sqrt{(6-9)^2 + (5-9)^2}$
Calculate $(6-9)^2$ : Calculate $(6-9)^2$ :
$(6-9)^2$
= $(-3)^2$
= $9$
Calculate $(5-9)^2$ : Calculate $(5-9)^2$ :
$(5-9)^2$
= $(-4)^2$
= $16$
Add Squares and Square Root: Now, add the squares of the differences and take the square root: $\sqrt{9 + 16}$ $\sqrt{25}$ $= 5$

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