Distance between Points on a Coordinate Plane Using Quadrant Signs & Absolute Value

Know the Signs of Each Quadrant! 5 4 3 2 1 - + + + - - + -

Point A is (-5, 3) Point B is (-2, 3) Point A is 3 units from Point B 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. Same Means Subtract A B 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 5 4 3 2 1

Point A is (3, 1) Point B is (3, -5) Point A is 6 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. Different Means Add 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 5 4 3 2 1 A B

Point A is 7 units from Point B Let’s Practice Point A is (-4, -3) Point B is (3, -3) Different Means Add 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 B A Point A is 7 units from Point B

Point A is 2 units from Point B Let’s Practice Point A is (-4, -3) Point B is (-2, -3) Same Means Subtract 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 B A 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!

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!

The distance between points is 7! (-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!

With the Coordinate Plane Without the Coordinate Plane You Try!! With the Coordinate Plane Without the Coordinate Plane (6, -3) & (12, -3) is: _____ (-5, -9) & (-5, 7) is: _____ (21, 0) & (-1, 0) is: _____ (-2, 5) & (-2, 1) is: _____ 5 4 3 2 1 B A 18 16 22 C D 4 What is the distance between A & B: ____ C & D: _____ B & C: ____ D & A: _____ 7 7 8 8