Question
Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.
Answers
Answered by
GPT-4o
To find the distance between the points \((2, 5)\) and \((7, 3)\), you can use the distance formula, which is derived from the Pythagorean Theorem:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substitute the coordinates \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\):
\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]
Calculate the differences:
\[
d = \sqrt{(5)^2 + (-2)^2}
\]
Square the differences:
\[
d = \sqrt{25 + 4}
\]
Add the results:
\[
d = \sqrt{29}
\]
Finally, take the square root of 29 and round to the nearest hundredth:
\[
d \approx 5.39
\]
So, the distance between the points \((2, 5)\) and \((7, 3)\) is approximately \( 5.39 \).
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Substitute the coordinates \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\):
\[
d = \sqrt{(7 - 2)^2 + (3 - 5)^2}
\]
Calculate the differences:
\[
d = \sqrt{(5)^2 + (-2)^2}
\]
Square the differences:
\[
d = \sqrt{25 + 4}
\]
Add the results:
\[
d = \sqrt{29}
\]
Finally, take the square root of 29 and round to the nearest hundredth:
\[
d \approx 5.39
\]
So, the distance between the points \((2, 5)\) and \((7, 3)\) is approximately \( 5.39 \).