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Learn how to determine the distance between two points on a coordinate plane using quadrant signs and absolute value. Practice subtracting and adding values based on the quadrant in which the points lie. Gain confidence in finding distances in different scenarios with or without a coordinate plane.
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Distance between Points on a Coordinate Plane Using Quadrant Signs & Absolute Value
Knowthe 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. Same Means Subtract A Point A is (-5, 3) Point B is (-2, 3) Point A & Point B are in the samequadrant, so I must subtract the absolute value of the different numbers. |-5| - |-2| = 5 – 2 = 3 Point A is 3 units from Point B B 5 4 3 2 1
DifferentMeans 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 samequadrant, 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
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 differentquadrants, 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
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 2units 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 • (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 D C 4 What is the distance between A & B: ____ C & D: _____ B & C: ____ D & A: _____ 7 7 8 8
