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.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

A B

Same Means Subtract

5

43

2

1

Different Means Add

*If two coordinate pairs are in different quadrants, then you need to

add the absolute value of the different numbers.

Point A is (3, 1) Point B is (3, -5)

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

A

B

Different Means Add

5

4

32

1

Let’s Practice

Point A is (-4, -3)Point B is (3, -3)

Different Means Add

A B

5

4

3

2

1

Point A & Point B are in different quadrants, so I must add the

absolute value of the different numbers.

|-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)

Same Means Subtract

A B

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.

|-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 – SubtractDifferent 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!!

1) (6, -3) & (12, -3) is: _____

2) (-5, -9) & (-5, 7) is: _____

3) (21, 0) & (-1, 0) is: _____

4) (-2, 5) & (-2, 1) is: _____

With the Coordinate Plane

Without the Coordinate Plane

What is the distance between A & B: ____ C & D: _____B & C: ____ D & A: _____

AB

C D

87

87

18

16

22

4

5

4

3

2

1