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)

Answer 1

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

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

Here, we have:
- \( (x_1, y_1) = (3, -5) \)
- \( (x_2, y_2) = (-2, -7) \)

Now, substituting the coordinates into the distance formula:

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

This simplifies to:

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

Calculating each term:

\[
(-5)^2 = 25, \quad (-2)^2 = 4
\]

Now add these values:

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

Next, we calculate \( \sqrt{29} \). The approximate value is:

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

Finally, rounding \( 5.385 \) up to the nearest tenth:

\[
\text{Rounded distance} \approx 5.4
\]

Therefore, the distance between the two points, rounded to the nearest tenth, is

\[
\boxed{5.4}
\]