To find the distance between the points $(1, -4)$ and $(-3, -2)$, we use the distance formula:

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

Where:

• $(x_1, y_1) = (1, -4)$
• $(x_2, y_2) = (-3, -2)$

Now, substitute the coordinates into the formula:

$d = \sqrt{(-3 - 1)^2 + (-2 + 4)^2}$ $d = \sqrt{(-4)^2 + (2)^2}$ $d = \sqrt{16 + 4}$ $d = \sqrt{20}$

The exact distance is $\sqrt{20}$. Simplifying $\sqrt{20}$:

$\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$

So, the exact distance is $2\sqrt{5}$.

Next, let's approximate this value to three decimal places:

$2\sqrt{5} \approx 2 \times 2.236 = 4.472$

Therefore, the distance between the points is:

• Exact: $2\sqrt{5}$
• Approximate: $4.472$

Would you like more details on this calculation, or do you have any other questions?

Related Questions:

1. What is the distance between points $(2, -3)$ and $(-1, 4)$?
2. How do you find the midpoint of two points?
3. What is the distance between $(0, 0)$ and $(3, 4)$?
4. Can you derive the distance formula from the Pythagorean theorem?
5. How do you find the distance between points in three dimensions?

Tip:

Always check if the square root can be simplified further to get the most exact form before approximating.