Parallel and Perpendicular Lines Investigation
This is applet is for investigating parallel and perpendicular lines.
[b]Parallel and Perpendicular Line Investigation[/b][br][br]1. Look at the three lines and their equations color coded [color=#c51414]red[/color], [color=#0a971e]green[/color] and [color=#1551b5]blue[/color].[br] Find the following:[br] [color=#c51414]Red Line[/color] m = ________ b = _________[br] [color=#1551b5]Blue Line[/color] m = ________ b = _________[br] [color=#0a971e]Green Line[/color] m = ________ b = ________[br][br] 2. Move Point B to [b](1, 4)[/b] and find the following:[br] [color=#c51414]Red Line[/color] m = ________ b = _________[br] [color=#1551b5]Blue Line[/color] m = ________ b = _________[br] [color=#0a971e]Green Line[/color] m = ________ b = ________[br][br]3. Move Point B to [b](3, 1)[/b] and find the following:[br][color=#c51414] Red Line[/color] m = ________ b = _________[br] [color=#1551b5]Blue Line[/color] m = ________ b = _________[br] [color=#0a971e]Green Line[/color] m = ________ b = ________[br][br]4. What do you notice about the [b]slopes (m)[/b] of the lines?[br] Slopes of parallel lines are ________________.[br] Slopes of perpendicular lines are _______________ and ________________.[br][br] 5. Move Point B to the [b]origin (0, 0)[/b] and write the equations for the:[br] [color=#c51414]Red Line[/color] [br] [color=#1551b5]Blue Line[/color] [br] [color=#0a971e]Green Line[/color][br][br]6. What conclusions can you make based on the equations from part 5?
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]