# Discovering the Midpoint Formula

Use the graph above to answer the questions below. Point C represents the midpoint of the segment.

1. Move the location of points A and B so that they represent new points on a HORIZONTAL LINE.  Record the ordered pairs below.

2. What is the value of the midpoint of the segment recorded on the line?

3. Use the x-coordinates of points A and B to calculate the x-coordinate of C. You can use any combination of numeric operations (+, -, x, ÷). Show your calculations in the answer box.

4. Use the y-coordinates of points A and B to calculate the y-coordinate of C. You can use any combination of numeric operations (+, -, x, ÷). Show your calculations in the answer box.

5. Move points A and B to represent new points on a VERTICAL LINE. Record the new ordered pairs below.

6. What is the value of the midpoint recorded? Explain how you can use the x-coordinates of points A and B to get the x-coordinates of point C. Explain how you can use the y-coordinates of points A and B to the y-coordinates of point C.

7. Move the location of points A and B so that they represent new points on an OBLIQUE LINE.  Record the ordered pairs below.

8. What is the value of the midpoint recorded? Explain how you can use the x-coordinates of points A and B to get the x-coordinates of point C. Explain how you can use the y-coordinates of points A and B to the y-coordinates of point C.

## Check for understanding:

9. Is calculating the midpoint of a horizontal and vertical line different than calculating the midpoint of an oblique line? Explain.

## Check for understanding:

10. Explain how to use the x-coordinates of any points A and B to calculate the x-coordinate of the midpoint C. You can use any combination of numeric operations (+, -, x, ÷). Show your calculations in the answer box.

## Check for understanding:

11. Explain how to use the y-coordinates of any points A and B to calculate the y-coordinate of the midpoint C. You can use any combination of numeric operations (+, -, x, ÷). Show your calculations in the answer box.

## Check for understanding:

12. Using your explanation above, calculate the midpoint of A(-2, 5) and B(7, -1). Show your calculations.

1. Use the grid below to plot point A(-2, 5) and B(7, -1). To label each point, as soon as you plot the point click the "AA" tool and choose "NAME AND LABEL".
2. Use the "line" tool to create a line segment.
3. Use the "point" tool to find the (midpoint or center) on the line segment.
4. Use the "point" tool, choose the point and click the "AA" tool to choose "NAME AND LABEL".
5.  Is your calculation from question 12 accurate?