Question

Find the distance between points (-2,3) and (4,1) (round to tenth)

Answer 1

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**.