Question
Find the distance between points (-2,3) and (4,1) (round to tenth)
Answers
Answered by
GPT-4o mini
To find the distance between the points \((-2, 3)\) and \((4, 1)\), we can use the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \((x_1, y_1) = (-2, 3)\) and \((x_2, y_2) = (4, 1)\).
Plugging in the coordinates:
\[
d = \sqrt{(4 - (-2))^2 + (1 - 3)^2}
\]
\[
d = \sqrt{(4 + 2)^2 + (1 - 3)^2}
\]
\[
d = \sqrt{(6)^2 + (-2)^2}
\]
\[
d = \sqrt{36 + 4}
\]
\[
d = \sqrt{40}
\]
\[
d = \sqrt{4 \times 10}
\]
\[
d = 2\sqrt{10}
\]
Calculating \(2\sqrt{10}\):
\[
\sqrt{10} \approx 3.162
\]
\[
2\sqrt{10} \approx 2 \times 3.162 \approx 6.324
\]
Rounding to the nearest tenth:
\[
d \approx 6.3
\]
Thus, the distance between the points \((-2, 3)\) and \((4, 1)\) is approximately **6.3**.
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Here, \((x_1, y_1) = (-2, 3)\) and \((x_2, y_2) = (4, 1)\).
Plugging in the coordinates:
\[
d = \sqrt{(4 - (-2))^2 + (1 - 3)^2}
\]
\[
d = \sqrt{(4 + 2)^2 + (1 - 3)^2}
\]
\[
d = \sqrt{(6)^2 + (-2)^2}
\]
\[
d = \sqrt{36 + 4}
\]
\[
d = \sqrt{40}
\]
\[
d = \sqrt{4 \times 10}
\]
\[
d = 2\sqrt{10}
\]
Calculating \(2\sqrt{10}\):
\[
\sqrt{10} \approx 3.162
\]
\[
2\sqrt{10} \approx 2 \times 3.162 \approx 6.324
\]
Rounding to the nearest tenth:
\[
d \approx 6.3
\]
Thus, the distance between the points \((-2, 3)\) and \((4, 1)\) is approximately **6.3**.
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