Coordinate Geometry Tools: Distance, Midpoint, Slope

Tim Brzezinski, Ronan Downes, Mar 4, 2020

Contains coordinate geometry applets.

Table of Contents

  1. Preliminary Topics
    1. Plotting Points (x,y): Dynamic Illustration
    2. Plotting Points (x,y): Quiz
    3. Rant Rant Rant Rant!
  2. Distance
    1. Distance in the Coordinate Plane (With Hints)
    2. Distance in the Coordinate Plane (II)
    3. Quiz: Distance in the Coordinate Plane (V1)
    4. Quiz: Distance in the Coordinate Plane (V2)
  3. Midpoint
    1. Midpoint and Endpoint Coordinates Action!
    2. Midpoint Coordinates (II)
    3. Midpoint (x,y) of a Segment in the Coordinate Plane (Quiz)
    4. Endpoint (x,y) of a Segment Given Midpoint & Other Endpoint
  4. Slope
    1. Graph to Slope Task
    2. Quick Slope Types Illustrator
    3. Slope: Quick Intuitive Quiz Questions
    4. Quick Quiz: Graphing Slope Types
    5. Slope: Intuitive Intro and Exploration
    6. Slope (Quiz) I
    7. Slope (Quiz) II
    8. Finding Slope Given 2 Points: Question Generator
    9. Parallel Consequence: Quick Reminder
    10. Parallel Consequence? (VA)
    11. Parallel Consequence? (VB)
    12. Parallel Lines in the Coordinate Plane (VA)
    13. Parallel Lines in the Coordinate Plane (VB)
    14. Special Pair of Lines in the Coordinate Plane
    15. Coordinate Geometry: Quick Investigation
    16. Parallel and Perpendicular Lines in the Coordinate Plane
    17. Perpendicular Lines in the CP: Quick Investigation
    18. Perpendicular Lines Investigation (VA)
    19. Perpendicular Lines Investigation (VB)
    20. Parallel & Perpendicular Consequence
    21. Slope Triangle Rotation (VA)
    22. Slope Triangle Rotation (VB)
  5. Angle Measures from Slopes
    1. Slope to Angle Measure Calculator (I)
    2. Slope to Angle Measure Calculator (II)
  6. Older Versions
    1. Distance in the Coordinate Plane (Quiz without Grid)
    2. Distance in the Coordinate Plane (Quiz With Grid)

1.

Preliminary Topics

  • 1. Plotting Points (x,y): Dynamic Illustration
  • 2. Plotting Points (x,y): Quiz
  • 3. Rant Rant Rant Rant!

1.1.

Plotting Points (x,y): Dynamic Illustration

[b][color=#000000]A COORDINATE is a NUMBER or a LETTER that indicates LOCATION. [/color][/b][color=#000000][br]Did you ever play Milton Bradley's game [/color][b][color=#000000]Battleship[/color][/b][color=#000000] as a kid? [br]If so, you dealt with coordinates! "A5" was either a "hit" or a "miss", right? [br]In this game, the "A" and the "5" are called coordinates. [br][br]Your mobile device can indicate your latitude and longitude. [br][b]LATITUDE and LONGITUDE[/b] are numbers that help tell a person his/her [b]LOCATION.[/b] [br]Thus, [b]LATITUDE and LONGITUDE[/b] are said to form a pair of [b]COORDINATES. [/b] [br] [br][/color]Note the coordinate plane below. [color=#0000ff]Press the [/color][color=#38761d]"New Example"[/color][color=#0000ff] button. After doing so press [/color][color=#bf9000]"Plot Point"[/color][color=#0000ff]. [br][/color]Be sure to watch the specific dynamics of how to plot a point correctly. Repeat the [b][color=#0000ff]colored step[/color][/b] above approximately 10 times. [color=#000000]Then, go to the link indicated below the applet. [/color]
[color=#000000]Once you're confident in your ability to plot a point given its coordintes, [url=https://www.geogebra.org/m/AbRPAY8V]click here[/url] to put into practice what you've just learned! [/color]
– Tim Brzezinski

1.2.

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1.3.

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2.

Distance

  • 1. Distance in the Coordinate Plane (With Hints)
  • 2. Distance in the Coordinate Plane (II)
  • 3. Quiz: Distance in the Coordinate Plane (V1)
  • 4. Quiz: Distance in the Coordinate Plane (V2)

2.1.

Distance in the Coordinate Plane (With Hints)

Discovery Lesson (Can be used without interactive figure below)
– Tim Brzezinski

2.2.

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2.3.

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2.4.

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3.

Midpoint

  • 1. Midpoint and Endpoint Coordinates Action!
  • 2. Midpoint Coordinates (II)
  • 3. Midpoint (x,y) of a Segment in the Coordinate Plane (Quiz)
  • 4. Endpoint (x,y) of a Segment Given Midpoint & Other Endpoint

3.1.

Midpoint and Endpoint Coordinates Action!

Here, point A is an endpoint and point M is a midpoint. Move A and M where you'd like and slide the slider to find the other endpoint (B).
– Tim Brzezinski

3.2.

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4.

Slope

  • 1. Graph to Slope Task
  • 2. Quick Slope Types Illustrator
  • 3. Slope: Quick Intuitive Quiz Questions
  • 4. Quick Quiz: Graphing Slope Types
  • 5. Slope: Intuitive Intro and Exploration
  • 6. Slope (Quiz) I
  • 7. Slope (Quiz) II
  • 8. Finding Slope Given 2 Points: Question Generator
  • 9. Parallel Consequence: Quick Reminder
  • 10. Parallel Consequence? (VA)
  • 11. Parallel Consequence? (VB)
  • 12. Parallel Lines in the Coordinate Plane (VA)
  • 13. Parallel Lines in the Coordinate Plane (VB)
  • 14. Special Pair of Lines in the Coordinate Plane
  • 15. Coordinate Geometry: Quick Investigation
  • 16. Parallel and Perpendicular Lines in the Coordinate Plane
  • 17. Perpendicular Lines in the CP: Quick Investigation
  • 18. Perpendicular Lines Investigation (VA)
  • 19. Perpendicular Lines Investigation (VB)
  • 20. Parallel & Perpendicular Consequence
  • 21. Slope Triangle Rotation (VA)
  • 22. Slope Triangle Rotation (VB)

4.1.

Graph to Slope Task

[color=#000000]Discovery Lesson Activity: [br][/color][color=#0000ff][b]Move the end points and observe how slope changes. [br][/b][/color]
How is the rise best described?
How is the run best described?
Under what conditions is the slope an integer?
When is the slope a unit fraction ( a unit fraction has a numerator of 1)
– Ronan Downes, Tim Brzezinski

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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4.13.

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4.14.

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4.15.

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4.16.

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4.17.

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4.18.

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4.19.

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4.20.

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4.21.

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4.22.

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5.

Angle Measures from Slopes

  • 1. Slope to Angle Measure Calculator (I)
  • 2. Slope to Angle Measure Calculator (II)

5.1.

Slope to Angle Measure Calculator (I)

[b]Students: [color=#1551b5]This applet is to be used when trying to use coordinate geometry prove two triangles (drawn in the coordinate plane) congruent.[/color] [/b][br][br][color=#c51414][i]You already know how to calculate the distance between any two points in the coordinate plane, so finding the length of any side of a triangle should be an easy task. [br]However, calculating the measure of an interior angle between two sides of a triangle is a bit more complicated.[/i][/color][br][br][color=#1551b5][b]If you need to calculate the angle measure between any two sides of a triangle, follow the directions in the applet below: [/b] [/color]
– Tim Brzezinski

5.2.

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6.

Older Versions

  • 1. Distance in the Coordinate Plane (Quiz without Grid)
  • 2. Distance in the Coordinate Plane (Quiz With Grid)

6.1.

Distance in the Coordinate Plane (Quiz without Grid)

[color=#c51414][b]Directions are contained in the applet below:[/b][/color]
– Tim Brzezinski

6.2.

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