Math worksheet for practicing the distance formula between two points on a coordinate plane.

Let's solve each problem step by step using the distance formula between two points:

📌 Distance Formula:

For two points $(x_1, y_1)$ and $(x_2, y_2)$, the distance is:
$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

But in some cases, if the points lie on a vertical or horizontal line, we can simplify:
- If $x_1 = x_2$: vertical line → distance = $|y_2 - y_1|$
- If $y_1 = y_2$: horizontal line → distance = $|x_2 - x_1|$

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🔹 Problem 1:

Points: $(2, 1)$ and $(2, 5)$

- Same $x$-coordinate → vertical line
- Distance = $|5 - 1| = 4$

✔ Answer: c. 4

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🔹 Problem 2:

Points: $(3, 4)$ and $(3, 1)$

- Same $x$-coordinate → vertical line
- Distance = $|4 - 1| = 3$

✔ Answer: c. 3

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🔹 Problem 3:

Points: $(4, 2)$ and $(4, 5)$

- Same $x$-coordinate → vertical line
- Distance = $|5 - 2| = 3$

✔ Answer: a. 3

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✔ Final Answers:

1. c. 4
2. c. 3
3. a. 3

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💡 Explanation:

All three pairs have the same $x$-coordinate, meaning they lie vertically on the same line. So, the distance is simply the absolute difference in their $y$-coordinates.

You can plot them on the graph:
- For example, $(2,1)$ and $(2,5)$ are both at $x=2$, one at $y=1$, the other at $y=5$ → 4 units apart.

This ensures the auto-pilot lands safely! ✈️

Let me know if you'd like to see the plotted points!