Find the midpoint of points A, left parenthesis, 10, comma, 9, right parenthesis*A*(10,9) and B, left parenthesis, 4, comma, 2, right parenthesis*B*(4,2) graphically.

To find the midpoint graphically between two points \(A(10, 9)\) and \(B(4, 2)\), you can follow these steps:

1. **Plot the Points**:
   - Start by plotting point \(A(10, 9)\) and point \(B(4, 2)\) on a coordinate plane. 
   - Point \(A(10, 9)\) is located 10 units to the right of the origin on the x-axis and 9 units up on the y-axis.
   - Point \(B(4, 2)\) is located 4 units to the right of the origin on the x-axis and 2 units up on the y-axis.

2. **Draw the Line Segment**:
   - Draw a straight line connecting points \(A\) and \(B\). This line segment represents the distance between the two points.

3. **Calculate the Midpoint Coordinates**:
   - The midpoint \(M\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
     \[
     M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
     \]

   - For points \(A(10, 9)\) and \(B(4, 2)\), substitute the coordinates into the midpoint formula:
     \[
     M = \left(\frac{10 + 4}{2}, \frac{9 + 2}{2}\right)
     \]
     \[
     M = \left(\frac{14}{2}, \frac{11}{2}\right)
     \]
     \[
     M = (7, 5.5)
     \]

4. **Plot the Midpoint**:
   - Plot the midpoint \(M(7, 5.5)\) on the graph. 
   - Point \(M(7, 5.5)\) is located 7 units to the right of the origin on the x-axis and 5.5 units up on the y-axis.
   
5. **Verify Graphically**:
   - The point \(M(7, 5.5)\) should be exactly halfway between points \(A(10, 9)\) and \(B(4, 2)\) on the graph, confirming that it is indeed the midpoint.

By following these steps graphically on a coordinate plane, you will visually determine that the midpoint \(M\) of points \(A(10, 9)\) and \(B(4, 2)\) is \((7, 5.5)\).

Would you like more details or have any other questions?

Here are some related questions you might find interesting:
1. How can you find the midpoint of three-dimensional coordinates?
2. How does finding the midpoint help in real-world applications, such as navigation or engineering?
3. What is the significance of the midpoint in geometry?
4. How would the midpoint change if one or both of the points were negative coordinates?
5. Can the concept of midpoint be applied to curves, and if so, how?

**Tip:** Graphically finding the midpoint involves averaging the x-coordinates and y-coordinates of the given points.

Learn how to find the midpoint graphically between points A(10, 9) and B(4, 2) on a coordinate plane. This problem involves plotting the points, drawing the line segment, calculating the midpoint coordinates using the midpoint formula, and verifying graphically. Suitable for students in Grades 7-9.

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