find the midpoint of the line: a= (-3,-3) b= (3,1)

To find the midpoint of the line segment connecting the points \(A(-3, -3)\) and \(B(3, 1)\), you can use the midpoint formula. The midpoint \((M)\) of a line segment with endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

For the given points \(A(-3, -3)\) and \(B(3, 1)\), we have:

\[ x_1 = -3, \quad y_1 = -3, \quad x_2 = 3, \quad y_2 = 1 \]

Plugging these values into the midpoint formula:

\[ M = \left( \frac{-3 + 3}{2}, \frac{-3 + 1}{2} \right) \]

Calculate each coordinate:

\[ M = \left( \frac{0}{2}, \frac{-2}{2} \right) \]
\[ M = (0, -1) \]

Therefore, the midpoint of the line segment connecting \(A(-3, -3)\) and \(B(3, 1)\) is \((0, -1)\).

Would you like more details or have any questions?

Here are 8 related questions to explore further:

1. How do you find the distance between two points in the coordinate plane?
2. What is the formula for finding the slope of a line segment between two points?
3. How can you determine if a point is the midpoint of a line segment?
4. What is the midpoint of the line segment with endpoints \((5, 2)\) and \((-1, 6)\)?
5. How do you find the equation of a line given two points?
6. What is the significance of the midpoint in geometry?
7. How can you use the midpoint formula in real-world applications?
8. What are some examples of problems where finding the midpoint is useful?

**Tip:** When using the midpoint formula, ensure you correctly add and divide the coordinates of the endpoints to avoid errors.

Learn how to find the midpoint of the line segment connecting the points (-3, -3) and (3, 1) using the midpoint formula. This problem involves basic coordinate geometry concepts and is suitable for students in Grades 7-9.

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