To determine the length of the line segment $PQ$ connecting $P(-2, 2)$ and $Q(0, -2)$, we use the distance formula:

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

Here:

• $P(x_1, y_1) = (-2, 2)$
• $Q(x_2, y_2) = (0, -2)$

Substituting the coordinates:

$PQ = \sqrt{(0 - (-2))^2 + (-2 - 2)^2}$

Simplify step by step:

1. $0 - (-2) = 2$
2. $-2 - 2 = -4$

So: $PQ = \sqrt{(2)^2 + (-4)^2}$

Square the terms: $PQ = \sqrt{4 + 16}$

Add them: $PQ = \sqrt{20}$

Simplify the square root: $PQ \approx 4.5 \, \text{(to 1 decimal place)}.$

Final Answer:

The length of $PQ$ is 4.5 units.

Do you need further clarification or a detailed breakdown of any step? Let me know!

Here are 5 related questions to explore:

1. How do you calculate the midpoint of a line segment?
2. Find the distance between $P(1, 3)$ and $Q(4, 7)$.
3. What is the distance between two points on a graph where one coordinate remains constant?
4. How is the Pythagorean theorem connected to the distance formula?
5. How do you determine if a triangle is a right triangle using the distance formula?

Tip: Always square the differences in coordinates before summing to avoid sign errors!