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.
13. Check your answer.
[list=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".[/*][*]Use the "line" tool to create a line segment. [/*][*]Use the "point" tool to find the (midpoint or center) on the line segment.[/*][*]Use the "point" tool, choose the point and click the "AA" tool to choose "NAME AND LABEL".[/*][*] Is your calculation from question 12 accurate?[br][/*][/list]