Coordinate plane and Reflection Rules

Coordinate plane and Reflection Rules

Lesson Goals

• Explore the coordinate plane

• Name the quadrants of a coordinate plane

• Describe each quadrant in terms of x and y

Quadrants

• The coordinate plane has 4 quadrants

• Quadrants are numbered counterclockwise starting with the top right.

• Quadrants may be seen written in Roman Numerals

• I, II, III, IV

• 1, 2, 3, 4

Multiple Choice

Which quadrant is shaded here?

• 1st quadrant

• 2nd quadrant

• 3rd quadrant

• 4th quarant

Multiple Choice

Which quadrant is shaded here?

• 1st quadrant

• 2nd quadrant

• 3rd quadrant

• 4th quarant

Multiple Choice

Which quadrant is shaded here?

• 1st quadrant

• 2nd quadrant

• 3rd quadrant

• 4th quarant

Multiple Choice

Which quadrant is shaded here?

• 1st quadrant

• 2nd quadrant

• 3rd quadrant

• 4th quarant

Multiple Select

Select all points in the fourth quadrant

• D

• E

• F

• G

• H

Multiple Select

Select all points in the third quadrant

• D

• E

• F

• G

• H

Multiple Select

Select all points in the second quadrant

• B

• C

• F

• G

• H

Multiple Choice

Which of these points is in the first quadrant?

• A

• B

• D

• H

Quadrant 1

• X coordinates are positive

• Y coordinates are positive

• Any point in quadrant 1 will have a positive x and positive y.

• (x,y) (+,+)

Quadrant 2

• x coordinates are negative

• y coordinates are positive

• Any point in quadrant 2 will have a negative x and positive y

• (-x,y) (-,+)

Quadrant 3

• x coordinates are negative

• y coordinates are negative

• Any point in quadrant 3 will have a negative x and negative y

• (-x,-y) (-,-)

Quadrant 4

• x coordinates are positive

• y coordinates are negative

• Any point in quadrant 4 will have a positive x and negative y

• (x,-y) (+,-)

Multiple Choice

Identify the quadrant where the point is located. (-2, 6)

• I

• II

• III

• IV

Multiple Choice

Identify the quadrant where the point is located. (10 , -5)

• I

• II

• III

• IV

Multiple Choice

Identify the quadrant where the point is located. (-3 , -4)

• I

• II

• III

• IV

Multiple Choice

Identify the quadrant where the point is located. (6 , 3)

• I

• II

• III

• IV

How does this help us with Transformations???

• Identify what quadrant the pre-image is in

• Determine what quadrant the image will be in after the transformation.

• What do we know about the x and y?

Think about this...

• What quadrant is the pre-image in?

• What are the signs? (+,+) (-,+) (-,-) or (+,-)

• What quadrant will your image be in?

• What are the signs? (+,+) (-,+) (-,-) or (+,-)

• Rule (+,+) -------> (+,-)

• x will stay positive.

• y will be negative.

Multiple Choice

What quadrant will L' be in after the reflection?

• I

• II

• III

• IV

Multiple Choice

What are the signs of the coordinates in quadrant III

• (+,+)

• (+,-)

• (-,+)

• (-,-)

Multiple Choice

Describe the image after the reflection.

• The coordinates of the image will be (+,+)

• The coordinates of the image will be (-,-)

• The coordinates of the image will be (-,+)

• The coordinates of the image will be (+,-)

Multiple Choice

If point L was at (4, -6) where would L' be located after a reflection over the y axis?

• (4,6)

• (-4,6)

• (-6,4)

• (-4,-6)

Multiple Choice

Give the reflection of the point across the given axis. (3, -6) , y axis.

• (-3, 6)

• (3, -6)

• (3, 6)

• (-3, -6)

Multiple Choice

Give the reflection of the point across the given axis. (-6, -10) , x axis.

• (6, 10)

• (6, -10)

• (-6, -10)

• (-6, 10)

Multiple Choice

The two points are reflections of each other across the x or y axis. Identify the axis. (-7, -1) and (7, -1)

• x

• y

Multiple Choice

The two points are reflections of each other across the x or y axis. Identify the axis. (5, 4) and (-5, 4)

• x

• y