DISTANCE BETWEEN POINTS
ON A COORDINATE PLANE
Using Quadrant Signs & Absolute Value
Know the Signs of Each Quadrant!
5
4
3
2
1
Same Means Subtract
*If two coordinate points are in the same quadrant,
then you need to subtract the absolute value of the
numbers that are different in the coordinate pairs.
5
4
3
2
1
Point A is (-5, 3)
Point B is (-2, 3)
Point A & Point B are in the same quadrant, so
I must subtract the absolute value of the
different numbers.
|-5| - |-2| =
5–2=3
Point A is 3 units from Point B
Different Means Add
*If two coordinate pairs are in different quadrants,
then you need to add the absolute value of the
different numbers.
5
Point A is (3, 1)
Point B is (3, -5)
4
3
2
1
Point A & Point B are in the same quadrant, so
I must subtract the absolute value of the
different numbers.
|1| + |-5| =
1+5=6
Point A is 6 units from Point B
Let’s Practice
Point A is (-4, -3)
Point B is (3, -3)
5
4
3
2
Point A & Point B are in different
quadrants, so I must add the absolute
value of the different numbers.
1
|-4| + |3| =
4+3=7
Point A is 7 units from Point B
Let’s Practice
Point A is (-4, -3)
Point B is (-2, -3)
5
4
3
2
Point A & Point B are in the same
quadrant, so I must subtract the
absolute value of the different numbers.
1
|-4| - |-2| =
4-2=2
Point A is 2 units from Point B
Let’s Try Without the Coordinate Plane
When we do not have a coordinate plane,
we use the quadrant signs to help us!
Remember the
Quadrant signs:
Figure out if the points are
in the same quadrant or in different quadrants.
by looking at the signs of the numbers.
For example: (2, -3) has a +2 and a -3, so it’s ++- means Quadrant 4.
Then follow the steps, we have already learned:
Same Quadrant – Subtract
Different Quadrants - Add
(9, -3) & (9, -11)
Are the points in the same quadrant?
(9, -3) is + (9, -11) is + -
Both points are + So both points are in the same quadrant!
(all points that are + - are in quadrant 4!)
(-3, -6) & (-11, -6)
Are the points in the same quadrant?
(-3, -6) is - (-11, -6) is - -
Both points are - So both points are in the same quadrant!
(all points that are - - are in quadrant 3!)
(-1, 5) & (6, 5)
Are the points in the same quadrant?
(-1, 5) is - +
(6, 5) is ++
One point is - +
The other point is + +
The combination of signs are different, so the points
are in different quadrants!
(all points that are - + are in quadrant 2!
all points that are ++ are in quadrant 1!)
Now…
Back to Finding Distance
between Two Points
without the Coordinate Plane
(9, -3) & (9, -11)
1) Are they in the same quadrant?
(9, -3) is + (9, -11) is + -
Yes!
2) Subtract the absolute value of the different numbers.
|-11| - |-3| =
11 – 3 = 8
The distance between points is 8!
(-3, -6) & (-11, -6)
1) Are they in the same quadrant?
(-3, -6) is - (-11, -6) is - -
Yes!
2) Subtract the absolute value of the different numbers.
|-11| - |-3| =
11 – 3 = 8
The distance between points is 8!
(-1, 5) & (6, 5)
1) Are they in the same quadrant?
(-1, 5) is - +
(6, 5) is ++
No!
2) Add the absolute value of the different numbers.
|-1| + |6| =
1+6=7
The distance between points is 7!
You Try!!
With the Coordinate Plane
Without the Coordinate Plane
5
4
3
1)
(6, -3) & (12, -3) is: _____
2)
(-5, -9) & (-5, 7) is: _____
3)
(21, 0) & (-1, 0) is: _____
4)
(-2, 5) & (-2, 1) is: _____
2
1
What is the distance between
A & B: ____
C & D: _____
B & C: ____
D & A: _____