Question

Fatou marks the points (3, -5) and (-2, -7) on the coordinate plane. Then, she finds the distance between them. What is the distance rounded up to the nearest tenth of a unit?

The distance is about ___ units

Answer 1

To find the distance between the two points \((3, -5)\) and \((-2, -7)\), we can use the distance formula:

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

Here, \((x_1, y_1) = (3, -5)\) and \((x_2, y_2) = (-2, -7)\).

First, we calculate the differences in the coordinates:

\[
x_2 - x_1 = -2 - 3 = -5
\]

\[
y_2 - y_1 = -7 - (-5) = -7 + 5 = -2
\]

Now we can plug these values into the distance formula:

\[
d = \sqrt{(-5)^2 + (-2)^2}
\]

Calculating the squares:

\[
d = \sqrt{25 + 4} = \sqrt{29}
\]

Now we need to calculate \(\sqrt{29}\).

Using a calculator, we find:

\[
\sqrt{29} \approx 5.385
\]

Rounding \(5.385\) to the nearest tenth gives:

\[
5.4
\]

Thus, the distance between the points \((3, -5)\) and \((-2, -7)\) rounded up to the nearest tenth of a unit is approximately:

\[
\boxed{5.4} \text{ units}
\]