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?

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

First, we calculate the differences in the x-coordinates and y-coordinates:

\[
x_2 - x_1 = -2 - 3 = -5
\]
\[
y_2 - y_1 = -7 - (-5) = -7 + 5 = -2
\]

Now we can substitute these values into the distance formula:

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

Calculating the squares:

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

Adding these together gives:

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

Next, we calculate \(\sqrt{29}\). The approximate value of \(\sqrt{29}\) is about \(5.385\).

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

\[
5.4
\]

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

\[
\boxed{5.4}
\]