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 \((-2, -7)\) on the coordinate plane, 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 \((x_2, y_2) = (-2, -7)\).

Now, substitute these values into the formula:

1. Calculate \(x_2 - x_1\):
\[
x_2 - x_1 = -2 - 3 = -5
\]

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

3. Now plug these values into the distance formula:
\[
d = \sqrt{(-5)^2 + (-2)^2}
\]

4. Calculate \((-5)^2\) and \((-2)^2\):
\[
(-5)^2 = 25 \quad \text{and} \quad (-2)^2 = 4
\]

5. Add these results:
\[
25 + 4 = 29
\]

6. Finally, take the square root:
\[
d = \sqrt{29}
\]

Next, we approximate \(\sqrt{29}\). The square root of 29 falls between the perfect squares of 25 and 36:

\[
5^2 = 25 \quad \text{and} \quad 6^2 = 36
\]

Calculating a more precise value, we find:

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

Rounding this to the nearest tenth, we get:

\[
\sqrt{29} \approx 5.4
\]

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

\[
\boxed{5.4}
\]