Distance in Cartesian Plane
Objectives
Start
Story
Distance along the same X-coordinate
Distance along the same Y-coordinate
Exploration in Geogebra
Summary
Story
Distance along same X-coordinate
Before we get started, let's draw on the Cartesian plane some points.
Follow the Instructions:
Next
1. In a grid paper draw the two axis of a cartesian plane.
2. Make ticks in x-axis and y-axis and label them with their numbers.
3. Plot points (4, 6) and (4, -3).
01:00
Distance between the two points is found just counting how many squares are between them!
For instance:
Distance between (4, 6) and (4, 2) is :
d=4,
Because there are 4 squares as seen in the figure.
If points have the same x-coordinate, distance is given by the absolute value of the y-coordinate difference.
For instance:
Distance between
(4, 6) and (4, 2) is :
d=|6-2|
d=4
Let's see some examples:
Example 1:
Find the distance between (2, 8) and (2, -3)
Example 2:
Find the distance between (-1, 6) and (-1, 1)
d= |6-1| = |5| = 5
d=5
d=11
Distance along the same Y-coordinate
Before moving on, let's draw another Cartesian plane with some points.
Try it by Yourself
Next
1. In a grid paper draw the two axis of a cartesian plane.
2. Make ticks in x-axis and y-axis and label them with their numbers.
3. Plot points (2, 5) and (11, 5).
4. Now, find the distance counting the squares between them
01:00
If points have the same y-coordinate, distance is given by the absolute value of the x-coordinate difference.
For instance:
Distance between
(2,5) and (11,5) is :
d=|11-2|
d=9
Try it by yourself:
Exploration in Geogebra
Follow the Instructions:
1. Open Geogebra
2. On text Input add points (2, 7) and (2, -1).
3. In tool bar, add a segment between points A and B
Follow the Instructions:
4.In Tool Bar click on "Distance or Length" Then click on the segment.
5. After clicking on the segment distance must appear.
Summary
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
6TH-DISTANCE-IN-CARTESIAN-PLANE-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MATERIAL
It is highly advised to have:
- Grid paper.
- Pencils of different colors.
- Eraser.
- A rule.
- Geogebra installed on your phone/tablet/computer (or use online version).
GEOMETRIC REASONING Standard 1: Apply previous understanding of the coordinate plane to solve problems. MA.6.GR.1.2 Find distances between ordered pairs, limited to the same x-coordinate or the same y-coordinate, represented on the coordinate plane. MA.6.GR.1.3 Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle. Number sense and Operations Standard 1: Extend previous understanding of numbers to define rational numbers. Plot,order and compare rational numbers. MA.6.NSO.1.4 Solve mathematical and real-world problems involving absolute value, including the comparison of absolute value.
MA6-WEEK12-DISTANCE-IN-CARTESIAN-PLANE
VIMSCHOOL
Created on April 25, 2024
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Transcript
Distance in Cartesian Plane
Objectives
Start
Story
Distance along the same X-coordinate
Distance along the same Y-coordinate
Exploration in Geogebra
Summary
Story
Distance along same X-coordinate
Before we get started, let's draw on the Cartesian plane some points.
Follow the Instructions:
Next
1. In a grid paper draw the two axis of a cartesian plane.
2. Make ticks in x-axis and y-axis and label them with their numbers.
3. Plot points (4, 6) and (4, -3).
01:00
Distance between the two points is found just counting how many squares are between them!
For instance:
Distance between (4, 6) and (4, 2) is :
d=4,
Because there are 4 squares as seen in the figure.
If points have the same x-coordinate, distance is given by the absolute value of the y-coordinate difference.
For instance:
Distance between
(4, 6) and (4, 2) is :
d=|6-2|
d=4
Let's see some examples:
Example 1: Find the distance between (2, 8) and (2, -3)
Example 2: Find the distance between (-1, 6) and (-1, 1)
d= |6-1| = |5| = 5
d=5
d=11
Distance along the same Y-coordinate
Before moving on, let's draw another Cartesian plane with some points.
Try it by Yourself
Next
1. In a grid paper draw the two axis of a cartesian plane.
2. Make ticks in x-axis and y-axis and label them with their numbers.
3. Plot points (2, 5) and (11, 5).
4. Now, find the distance counting the squares between them
01:00
If points have the same y-coordinate, distance is given by the absolute value of the x-coordinate difference.
For instance:
Distance between
(2,5) and (11,5) is :
d=|11-2|
d=9
Try it by yourself:
Exploration in Geogebra
Follow the Instructions:
1. Open Geogebra
2. On text Input add points (2, 7) and (2, -1).
3. In tool bar, add a segment between points A and B
Follow the Instructions:
4.In Tool Bar click on "Distance or Length" Then click on the segment.
5. After clicking on the segment distance must appear.
Summary
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
6TH-DISTANCE-IN-CARTESIAN-PLANE-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MATERIAL
It is highly advised to have:
GEOMETRIC REASONING Standard 1: Apply previous understanding of the coordinate plane to solve problems. MA.6.GR.1.2 Find distances between ordered pairs, limited to the same x-coordinate or the same y-coordinate, represented on the coordinate plane. MA.6.GR.1.3 Solve mathematical and real-world problems by plotting points on a coordinate plane, including finding the perimeter or area of a rectangle. Number sense and Operations Standard 1: Extend previous understanding of numbers to define rational numbers. Plot,order and compare rational numbers. MA.6.NSO.1.4 Solve mathematical and real-world problems involving absolute value, including the comparison of absolute value.