Find the midpoint of points A(-7,-8) and B(3,2) Graphically

To find the midpoint of points \( A(-7, -8) \) and \( B(3, 2) \) graphically, we first calculate the midpoint using the midpoint formula:

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

For points \( A(-7, -8) \) and \( B(3, 2) \):

\[
\text{Midpoint} = \left( \frac{-7 + 3}{2}, \frac{-8 + 2}{2} \right) = \left( \frac{-4}{2}, \frac{-6}{2} \right) = \left( -2, -3 \right)
\]

### Steps to Graphically Find the Midpoint:

1. **Plot the Points**: Mark the points \( A(-7, -8) \) and \( B(3, 2) \) on a coordinate plane.
2. **Draw the Line Segment**: Draw a straight line connecting points \( A \) and \( B \).
3. **Locate the Midpoint**: The midpoint \((-2, -3)\) will be located exactly halfway along this line segment.

If you'd like a visual representation of this, I can generate a graph for you. Would that be helpful?

Here are some additional questions you might consider:

1. How do you derive the midpoint formula?
2. What is the significance of a midpoint in dividing a line segment?
3. How can you verify the midpoint using a ruler and the graph?
4. How does the slope of the line segment relate to the midpoint?
5. What other geometrical properties can be determined by knowing the midpoint?

**Tip:** When plotting points on a graph, use consistent scales on the x and y axes to ensure accuracy in locating the midpoint.

Learn how to find the midpoint of points A(-7, -8) and B(3, 2) graphically with step-by-step instructions and a detailed explanation. This problem involves using the midpoint formula in coordinate geometry to locate the midpoint of a line segment. Suitable for students in Grades 9-10.

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