The problem asks us to find the distance between the two points $(1, -3)$ and $(-7, 2)$, and round the answer to the nearest tenth.

1. Problem Description

The problem asks us to find the distance between the two points $(1, -3)$ and $(-7, 2)$, and round the answer to the nearest tenth.

2. Solution Steps

We can use the distance formula to find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$:

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

In this case, we have $(x_1, y_1) = (1, -3)$ and $(x_2, y_2) = (-7, 2)$. Plugging these values into the distance formula, we get:

$d = \sqrt{(-7 - 1)^2 + (2 - (-3))^2}$

$d = \sqrt{(-8)^2 + (5)^2}$

$d = \sqrt{64 + 25}$

$d = \sqrt{89}$

Now, we need to find the approximate value of $\sqrt{89}$ and round to the nearest tenth.

We know that $9^2 = 81$ and $10^2 = 100$. Thus, $\sqrt{89}$ is between 9 and

1

0. Since 89 is closer to 81 than 100, we can expect the value to be closer to

9.

$\sqrt{89} \approx 9.433981132...$

Rounding to the nearest tenth, we get 9.

4.

3. Final Answer

9. 4