1. Finding Coordinate Plane Distance…
WITHOUT THE COORDINATE PLANE

2. To find the distance between two points, count the units between them.

3. There is another way to find the distance, without counting units.
First, we need to know the following things:
Points with the SAME x-coordinates are on the same VERTICAL line.
Points with the SAME y-coordinates are on the same HORIZONTAL line.
We use absolute values to find the distance between two points.
**Remember**
Distance is ALWAYS positive!

4. Using Absolute Value to Calculate Distance
Decide if the points are in the same or different quadrants
Same Quadrants—x-coordinates are both positive or both negative AND y-coordinates are both positive or both negative
Examples: (2, -5) and (2, -3) (4, 6) and (4, 1)
(-1, 5) and (-3, 5) (-3, -9) and ( -7, -9)
Different Quadrants—x-coordinates are NOT both positive or negative OR y-coordinates are NOT both positive or negative
Examples: (-2, -5) and (2, 3) (-4, 6) and (4, -1)
(-1, 5) and (3, 5) (-3, 9) and (7, -9)

5. Same Quadrant? Different Quadrant?
(10, 2) and (12, 2) (-1, 2) and (-1, -8) (5, -7) and (9, -7) (-14, -2) and (-16, -2) (-8, 4) and (-8, -3)
Same
Different
For students who need to practice step by step

6. If the points are in the SAME quadrants, SUBTRACT the coordinates that are different.
SAME QUADRANT= SUBTRACT
Example: (4, 5) and (4, 9)
The x-coordinates are the same - Ignore them!
The y-coordinates are different - SUBTRACT them!
These two points are 4 units apart.

7. If the points are in the DIFFERENT quadrants, ADD the coordinates that are different.
DIFFERENT QUADRANT = ADD
***Remember: Use the absolute value of the numbers!!
Example: (-4, -5) and (-4, 9)
The x-coordinates are the same. Ignore them!
The y-coordinates are different. ADD them!
These two points are 14 units apart.

8. What is the distance between these two points?
(-2, 3) and (2, 3) What coordinates the same? Ignore them! Add or subtract the coordinates that are different. Distance is 4 units
Same Quadrant or Different Quadrant?

9. What is the distance between these two points?
(-4, -6) and (4, -6) What coordinates the same? Ignore them! Add or subtract the coordinates that are different. Distance is 8 units
Same Quadrant or Different Quadrant?

10. What is the distance between these two points?
(2, -1) and (2, -4) What coordinates the same? Ignore them! Add or subtract the coordinates that are different. Distance is 3 units
Same Quadrant or Different Quadrant?

11. Coordinate Plane Distance:
( 2, -3) and (2, 5)
What is the distance between these two points?
│-3│ │5│ 8

12. Coordinate Plane Distance:
( -4, 5) and (-4, 8)
What is the distance between these two points?
│8│ │5│ 3

13. Coordinate Plane Distance:
( 9, -4) and (9, 2)
What is the distance between these two points?
│-4│ │2│ 6

14. Coordinate Plane Distance:
( -1, -3) and (-1, -5)
What is the distance between these two points?
│-5│ │-3│ 2

15. Coordinate Plane Distance:
( 8, -7) and (8, -1)
What is the distance between these two points?
│-7│ │-1│ 6

16. Coordinate Plane Distance:
( -2, -6) and (-2, 3)
What is the distance between these two points?
│-6│ │3│ 9

17. Coordinate Plane Distance:
( 2, -3) and (2, 5)
What is the distance between these two points?
│-3│ │5│ 8

18. How would you find the distance between (-3, 0) and (-3, 9)?

19. Stop Here

20. Name two points that are 3 points away from: (2, 6)
( 2, ___) (2, ___) 9 3

21. Name two points that are 1 point away from: (2, 5)
( ___, 5) 3 1

22. Name two points that are 2 points away from: (4, -2)
( 4, ___) (4, ___) -4

23. Name two points that are 1 point away from: (-3, -2)
( ___, -2) -2 -4

24. Name two points that are 4 points away from: (3, -5)
( 3, ___) (3, ___) -9 -1

25. Find the distance between the following points:
(4, -1) and (4, 5)
(9, -7) and (4, -7)
(-4, -6) and (4, -6)
(-3, -1) and (8, -1)
(7, 9) and (7, 1)
(10, -2) and (-1, -2
(8, 2) and (0, 2)
(-9, -1) and (-9, -7)
(7, -8) and (7, 5)
(14, -14) and (14, 25)