Question

Question
Fatou marks the points (3,−5)
and (−2,−7)
on the coordinate plane. Then, she finds the distance between them. What is this distance rounded up to the nearest tenth of a unit?(1 point)
The distance is about
units.

Answer 1

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

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

Where:
- \((x_1, y_1) = (3, -5)\)
- \((x_2, y_2) = (-2, -7)\)

Substituting the coordinates into the formula gives us:

\[
d = \sqrt{((-2) - 3)^2 + ((-7) - (-5))^2}
\]

Calculating inside the parentheses:

\[
d = \sqrt{(-5)^2 + (-2)^2}
\]
\[
d = \sqrt{25 + 4}
\]
\[
d = \sqrt{29}
\]

Now, calculating \(\sqrt{29}\):

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

Rounding this to the nearest tenth:

\[
\text{Distance} \approx 5.4 \text{ units}
\]

Thus, the distance is about **5.4 units**.