10-2 : use absolute value to find distance on a coordinate plane

Distance On the Coordinate Plane

_{I can determine vertical or horizontal distances on the coordinate plane.}

​ABSOLUTE VALUE

​Absolute Value means

DISTANCE FROM ZERO.

​ABSOLUTE VALUE

​The absolute value of 3 and -3 is 3. They are both 3 units aways from 0.

Multiple Choice

Distance is always a ______ number.

• Negative

• Positive

• Positive or Negative

Multiple Choice

So, distance should NEVER have a ______ answer.

• Positive

• Negative

The 4 Quadrants

• Quadrant I = ( + , + )

• Quadrant II = ( - , + )

• Quadrant III = ( - , - )

• Quadrant IV = ( + , - )

Multiple Choice

Quadrant I has what signs?

• ( + , + )

• ( - , - )

• ( + , - )

• ( - , + )

Multiple Choice

Quadrant IV has what signs?

• ( + , + )

• ( - , - )

• ( + , - )

• ( - , + )

Multiple Choice

Quadrant III has what signs?

• ( + , + )

• ( - , - )

• ( + , - )

• ( - , + )

Multiple Choice

Quadrant II has what signs?

• ( + , + )

• ( - , - )

• ( + , - )

• ( - , + )

Multiple Choice

Are these two points in the same quadrant? Or different?

( -2 , 3 ) and ( 6 , -7)

• Same Quadrant

• Different Quadrant

Multiple Choice

Are these two points in the same quadrant? Or different?

( 10 , 4 ) and ( 3 , 4)

• Same Quadrant

• Different Quadrant

Multiple Choice

Are these two points in the same quadrant? Or different?

( 9 , -2 ) and ( 8 , -2)

• Same Quadrant

• Different Quadrant

Same Quadrant? Subtract!

• We can find the distance between points that lie in the same quadrant, like the Ferris Wheel and the Rollercoaster, using subtraction.

• The Rollercoaster is at (5, 2)

• The Ferris Wheel is at (5, 6)

• |6| - |2| = 6 - 2 = 4

• The Ferris Wheel and Rollercoaster are 4 spaces apart.

Find the distance between these two points using subtraction.

( 3 , 6 ) and ( 3 , 11 )

_{Make sure to subtract their ABSOLUTE VALUES.}

Find the distance between these two points using subtraction.

( 3 , 6 ) and ( 3 , 11 )

|11| - |6| = 11 - 6 = 5

_{Make sure to subtract their ABSOLUTE VALUES.}

Multiple Choice

Find the distance between these two points using subtraction. ^{(Remember to use their ABSOLUTE values!)}

( -2 , 10 ) and ( -5 , 10 )

• 3

• -3

• 7

• -7

Multiple Choice

Find the distance between these two points using subtraction. ^{(Remember to use their ABSOLUTE values!)}

( 8 , 4 ) and ( 8 , 22 )

• 26

• -26

• 18

• -18

Multiple Choice

Find the distance between these two points using subtraction. ^{(Remember to use their ABSOLUTE values!)}

( -11 , -3 ) and ( -2 , -3 )

• 13

• 9

• -9

• -13

Different Quadrant? Add!

• We can find the distance between points that lie in the different quadrants, like the Restrooms and the Water Slide, using addition.

• The Restrooms are at ( 4 , -4 )

• The Water Slide is at ( -3 , -4 )

• |4| + |-3| = 4 + 3 = 7

• The restrooms and water slide are 7 spaces apart.

Find the distance between these two points using addition.

( 5 , -2 ) and ( -3 , -2)

_{Make sure to add their ABSOLUTE VALUES!}

Find the distance between these two points using addition.

( 5 , -2 ) and ( -3 , -2)

|5| + |-3| = 5 + 3 = 8

_{Make sure to add their ABSOLUTE VALUES!}

Multiple Choice

Find the distance between these two points using addition.

( 10 , -2 ) and ( -3 , -2)

• 13

• -13

• 7

• -7

Multiple Choice

Find the distance between these two points using addition.

( -4 , -4 ) and ( 7 , -4 )

• 3

• -11

• -3

• 11

Multiple Choice

Find the distance between these two points using addition.

( 5 , -8 ) and ( 5 , 12 )

• -20

• 20

• 4

• -4

Multiple Choice

Determine if these points are in the same quadrant or different quadrants. Then find the distance using the right strategy.

_{Same = Subtract , Different = aDD}

( 2 , 10 ) and ( 5 , 10 )

• Same, 3

• Same, 7

• Different, 3

• Different, 7

Multiple Choice

Determine if these points are in the same quadrant or different quadrants. Then find the distance using the right strategy.

_{Same = Subtract , Different = aDD}

( -8 , -2 ) and ( 5 , -2 )

• Same, -13

• Same, 13

• Different, -13

• Different, 13

Multiple Choice

Determine if these points are in the same quadrant or different quadrants. Then find the distance using the right strategy.

_{Same = Subtract , Different = aDD}

( 1 , 15 ) and ( 1 , -21 )

• Same, -36

• Same, 36

• Different, -36

• Different, 36

Multiple Choice

What is the distance between point A and point C?

• 5

• 6

• 3

• 1

Multiple Choice

What is the distance between point A and point B?

• 2

• 3

• 4

• 5

Multiple Choice

What is the distance between points B and D?

• 7

• 17

• 4

• 5

Multiple Choice

What is the distance between points C and D?

• 3

• 5

• 4

• 2

Multiple Choice

Find the distance between (0, 6) and (0, -4)

• 2

• -2

• 0

• 10

Multiple Choice

What is the distance between points  (5, 5) and  (1, 5) on a coordinate plane?

• -4

• 4

• 10

• -10

Multiple Choice

What is the distance between points (-7, 8) and (2, 8)?

• 4 units

• 5 units

• 3 units

• 9 units

Multiple Choice

What is the distance between points (3, -5) and (3, -8)?

• 1 unit

• 2 units

• 3 units

• 4 units