Question

Find the distance between the points (0.6,3.2) and (3.2,-0.6)



Give the approximate distance, rounded to three decimal places.

Answer 1

To find the distance between the points \((0.6, 3.2)\) and \((3.2, -0.6)\), we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Given the points:
- \( (x_1, y_1) = (0.6, 3.2) \)
- \( (x_2, y_2) = (3.2, -0.6) \)

We compute the differences:
- \( x_2 - x_1 = 3.2 - 0.6 = 2.6 \)
- \( y_2 - y_1 = -0.6 - 3.2 = -3.8 \)

Now we square these differences:
- \( (x_2 - x_1)^2 = (2.6)^2 = 6.76 \)
- \( (y_2 - y_1)^2 = (-3.8)^2 = 14.44 \)

Now we can plug these values into the distance formula:

\[
d = \sqrt{6.76 + 14.44} = \sqrt{21.20}
\]

Calculating the square root:

\[
d \approx 4.605
\]

Rounding this to three decimal places, we get:

\[
d \approx 4.605
\]

Thus, the approximate distance between the points \((0.6, 3.2)\) and \((3.2, -0.6)\) is \(\boxed{4.605}\).