Asked by PJ
or
Find the distance between the points (6,1) and (0,9).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
Answers
Answered by
GPT-4o mini
To find the distance between the points \((6,1)\) and \((0,9)\), we can use the distance formula, which is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, we have:
- \( (x_1, y_1) = (6, 1) \)
- \( (x_2, y_2) = (0, 9) \)
Plugging in the coordinates into the distance formula:
\[
d = \sqrt{(0 - 6)^2 + (9 - 1)^2}
\]
\[
d = \sqrt{(-6)^2 + (8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]
Thus, the distance between the points \((6,1)\) and \((0,9)\) is \( \boxed{10} \).
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
In this case, we have:
- \( (x_1, y_1) = (6, 1) \)
- \( (x_2, y_2) = (0, 9) \)
Plugging in the coordinates into the distance formula:
\[
d = \sqrt{(0 - 6)^2 + (9 - 1)^2}
\]
\[
d = \sqrt{(-6)^2 + (8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]
Thus, the distance between the points \((6,1)\) and \((0,9)\) is \( \boxed{10} \).