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Calculate the distance between point (-3,2) and point (1,2) in Quadrants I and II.

To calculate the distance between the points \((-3,2)\) and \( (1,2) \), we can use the distance formula:

\[
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case:
- \(x_1 = -3\)
- \(y_1 = 2\)
- \(x_2 = 1\)
- \(y_2 = 2\)

Substitute these values into the distance formula:

\[
\text{Distance} = \sqrt{(1 - (-3))^2 + (2 - 2)^2}
\]

Simplify inside the square root:

\[
\text{Distance} = \sqrt{(1 + 3)^2 + 0^2}
\]

\[
\text{Distance} = \sqrt{4^2 + 0}
\]

\[
\text{Distance} = \sqrt{16}
\]

\[
\text{Distance} = 4
\]

So, the distance between the points \((-3, 2)\) and \( (1, 2) \) is \(4\) units.

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. What is the distance between the points \((2, 1)\) and \((3, -3)\)?
2. How do you find the midpoint between two points on a coordinate plane?
3. What is the distance between the origin \((0, 0)\) and the point \((3, -3)\)?
4. Can you derive the distance formula from the Pythagorean theorem?
5. What is the distance between \((1, 2)\) and \((2, 1)\)?
6. How do you calculate the distance between two points in 3D space?
7. What is the distance between the points \((-1, -3)\) and \((3, -3)\)?
8. How would the distance formula change if you are working in polar coordinates?

**Tip:** Always double-check the coordinates you are substituting into the distance formula to avoid any errors.

Learn how to calculate the distance between the points (-3, 2) and (1, 2) using the distance formula in coordinate geometry. This problem involves applying the distance formula to find the distance between two points on a coordinate plane. Suitable for students in Grades 6-8.

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