Quarter 1 and Quarter 2

Coordinate Plane Transformations

Open Ended

What does it mean to transform something?

Translations

• Are a type of transformation that move a shape (by shifting or sliding) to another location

• Can move an image left, right, up, or down

• The pre-image is the original image and the image is the image after it has been transformed
  

• Make note of the notation used for the pre-image and image

Open Ended

What else did you notice about the pre-image and image? What do you wonder?

How do we "perform" transformations in the coordinate plane?

Multiple Choice

Point Q is located at (4, 5). We want to shift it 6 units right. What would be the location of point Q'?

• (10, 5)

• (5, 10)

• (4, 11)

• (11, 4)

• I'm not sure, I need more explanation.

Multiple Choice

Point K is located at (-2, 0). We want to shift it down 3 units. What would be the location of point Q'?

• (-5, 0)

• (0, -3)

• (-2, -3)

• (-5, -3)

• I'm not sure, I need more explanation.

Poll

On the graph shown, the point R' was created by moving point R _____________.

• 6 units left

• 6 units right

• 4 units up

• 4 units down

Mapping Notation

Instead of writing x units left/right and y units up/down, we can use mapping notation. The number being added or subtracting to each coordinate let's you know how many units to move AND in what direction.

Open Ended

What is the meaning of the notation in relation to translations? 

$$\left(x,\ y\right)\rightarrow\ \left(x-3,\ y+6\right)$$  

Multiple Choice

Which notation denotes a translation of a pre-image 5 units right and 2 units down?

• $$T_{\left(-5,\ 2\right)}$$

• $$T_{\left(-2,5\right)}$$

• $$T_{\left(5,-2\right)}$$

• $$T_{\left(-2,\ -5\right)}$$

We want to reflect the triangle over the x-axis.

When creating a reflection, each point is the same distance from the line of reflection.

​

​Consider ΔXYZ

Notice:

1. point X is 3 units from the x-axis

2. point Y is 1 unit from the x-axis

3. point Z is 5 units from the x-axis

​

​Consider ΔXYZ

Multiple Select

If I reflect ΔXYZ across the x-axis, what is the first step to drawing the reflection?

• Connect all of the dots

• Plot each new point the same number of units from the line of reflection

• Count the number of units each point is from the line of reflection

Multiple Choice

If I reflect ΔXYZ across the x-axis, what is the second step to drawing the reflection?

• Connect all of the dots

• Plot each new point the same number of units from the line of reflection

• Count the number of units each point is from the line of reflection

Multiple Choice

Quadrilateral J is reflected over the x-axis. What is the image of the reflection?

• F

• G

• H

• Not shown

Multiple Choice

Which two quadrilaterals are reflections of each other across the y-axis?

• F and G

• G and H

• H and J

• F and J

Multiple Choice

How are quadrilaterals H and J related?

• They are reflections across the y-axis

• They are rotations around the origin.

• They are translations of each other.

Multiple Choice

What axis is the triangle being reflected over?

• X-axis

• Y-axis

Multiple Choice

What axis is the image reflected over?

• X-axis

• Y-axis

Rotations

Multiple Choice

What type of rotation does this represent (from red to blue)?

• 270⁰ clockwise

• 180⁰

• 90⁰ clockwise

Multiple Choice

If you were to rotate ABCD 180° about the origin, what would the coordinate of A' be?

• (-5, 5)

• (-3, -5)

• (-5, 3)

• (-3, 3)

Multiple Choice

Rotation Rules (clockwise):

180^o rotation: (x, y)→(-x, -y)

What are the coordinates of C' after a rotation of 180° clockwise?

• (-3, -1)

• (3,1)

• (1,3)

• (-1, -3)

Multiple Choice

Rotation Rules (clockwise):

90^o rotation: (x, y)→(y, -x)

What are the coordinates for A' after a 90^⁰ rotation clockwise?

• (1, 3)

• (3, 1)

• (3, -1)

• (1, -3)

Multiple Choice

Rotation Rules (clockwise):

270^o rotation: (x, y)→(-y, x)

What are the coordinates of B' after a 270° clockwise?

• (4, 4)

• (4, -4)

• (-3, 4)

• (-4, 4)

Multiple Choice

Triangle A is rotated 270° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

A dilation is which of the following:

• only an enlargement

• only a reduction

• either an enlargement or a reduction

• neither an enlargement nor a reduction

Multiple Choice

A dilation always produces a congruent figure.

• True

• False

Multiple Choice

A dilation always produces a similar figure. Similar figures have the same ______ but different ______.

• measure; shapes

• sizes; shapes

• value; measures

• shape; sizes

Multiple Choice

Did the image enlarge, reduce or none of the above?

• Enlarge

• Reduce

• None of the above

Multiple Choice

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

• B' (2 , 4.5)

• B' (-8 ,-18)

• B' (8 ,18)

• B' (9 ,4)

Multiple Choice

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)

Multiple Choice

Two trapezoids are shown on the coordinate grid. Which sequence of transformations shows that the two trapezoids are congruent

• Reflect Trapezoid 1 across the x-axis, then reflect the resulting figure across the y-axis.

• Translate Trapezoid 1 to the right 4 units, then reflect the resulting figure across the x-axis.

• Translate Trapezoid 1 to the right 4 units, then translate the resulting figure down 4 units.

• Translate Trapezoid 1 down 4 units, then reflect the resulting figure across the x-axis.

Multiple Choice

Two triangles are shown on the coordinate grid. Which sequence of transformation shows that  $$\Delta ABC\cong\Delta DEF$$  ?

• Reflect △ABC across the x-axis, then translate it down 2

• Reflect △ABC across the y-axis, then translate it down 2

• Reflect △ABC across the x-axis, then translate it up 2

• Reflect △ABC across the y-axis, then translate it up 2

Multiple Choice

Two triangles are shown on the coordinate grid. Which sequence of transformations shows that

$$\Delta ABC\cong\Delta DEF$$  

• Reflect △ABC across the x-axis, then translate it down 1

• Reflect △ABC across the x-axis, then translate it up 1

• Reflect △ABC across the y-axis, then translate it down 1

• Reflect △ABC across the y-axis, then translate it up 1

Multiple Select

What type of angles are these? (select 2)

• Adjacent Angles

• Vertical Angles

• Complementary Angles

• Supplementary Angles

Multiple Choice

Which function is linear?

• y = 2x + 4
• y = 2x² + 4
• y = 2x(4 − 3x)
• xy = 15

Multiple Choice

Is function represented by the table linear or nonlinear?

• linear
• nonlinear

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

Is the function linear or nonlinear?

• Linear Function
• Nonlinear Function

Multiple Choice

How many solutions would this system of equations have?

• No Solution

• One Solution

• Infinite Solutions

Multiple Choice

How many solutions would this system of equations have?

• No Solution

• One Solution

• Infinite Solutions

Multiple Choice

How many solutions would this system of equations have?

• No Solution

• One Solution

• Infinite Solutions

Multiple Choice

How many solutions would this system of equations have?

• No Solution

• One Solution

• Infinite Solutions

Multiple Choice

How many solutions would this system of equations have?

• No Solution

• One Solution

• Infinite Solutions

Multiple Choice

-7w + 4 = -3(w + 3) - 2(w + 1)

• No Solution

• One Solution

• Infinite Solution

Multiple Choice

What is the constant of proportionality (slope)?

• $3

• $4

• $2

• $9

Multiple Choice

Which angles are vertical angles?

• $$\angle8\ \&\ \angle7$$

• $$\angle8\ \&\ \angle6$$

• $$\angle8\ \&\ \angle5$$

Multiple Choice

What is the Constant of Proportionality (slope)?

• m=46

• m=92

• m=276

• no slope

Multiple Choice

Which angle is a vertical angle to with $$\angle7$$  ?

• $$\angle1$$  

• $$\angle5$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle9$$  

Multiple Choice

Find the slope:

• 3/4
• 4/3
• -3/4
• -4/3

Multiple Choice

Angle 1 and Angle 5 are examples of which type of angle pair?

• Alternate exterior angles

• Alternate interior angles

• Vertical angles

• Corresponding angles

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2
• 3
• 5
• Cannot be Determined 

Multiple Choice

Which of the following angles would NOT be congruent to the measure of $$\angle7$$ ?

• $$\angle2$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle8$$  

Multiple Choice

Find the slope.

• ¹/₄
• 4
• -¹/₄
• -4

Multiple Choice

Which of the following is NOT an example of supplementary angles?

• $$\angle7\ and\ \angle8$$  

• $$\angle2\ and\ \angle3$$  

• $$\angle1\ and\ \angle7$$  

• $$\angle6\ and\ \angle4$$  

Multiple Choice

Find the slope.

• -2
• 2
• ¹/₂
• -¹/₂

Multiple Choice

If the  $$m\angle7\ =\ 115\degree,$$  find the measure of  $$\angle2.$$  

• $$115\degree$$  

• $$65\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

Find the slope between the two points.
(3, 7) and (-4, 2)

• ⁷/₅
• ⁵/₇
• ²/₃
• 2

Multiple Choice

Angles 4 and 6 are...

• supplementary

• congruent

Multiple Choice

Find the slope.

• ²/₅
• ^-2/₅
• ⁵/₂
• ^-5/₂

Multiple Choice

Supplementary Angles add up to be ______-degrees

• 270

• 180

• 90

• 120

Multiple Choice

Find the slope between the two points.

(3, 2) and (5, 8)

• ^-1/₆

• 3

• ¹/₆

• 6

Multiple Choice

Complementary Angles are two angles that add up to equal _____-degrees

• 180

• 90

• 270

• 120

Multiple Choice

Find the slope between the two points.
(2, 7) and (5, 8)

• ¹/₃
• ^-1/₃
• 3
• -3

Multiple Choice

1) Given the two parallel lines cut by a transversal.

What is the vertical angle to angle 4?

• Angle 2

• Angle 6

• Angle 8

• Angle 7

Multiple Choice

Slope is written as a(n) ________.

• Ordered Pair (x, y)
• Fraction

Multiple Choice

If the  $$m\angle5\ =\ 63\degree,$$  find the measure of  $$\angle3.$$  

• $$63\degree$$  

• $$117\degree$$  

• $$180\degree$$  

• Cannot be determined

Multiple Choice

The line pictured has a(n) ______ slope.

• Undefined
• Zero
• Positive
• Negative

Multiple Choice

• 41°
• 65°
• 102°
• 115°

Multiple Choice

The line pictured has a(n) ______ slope.

• Undefined
• Zero
• Positive
• Negative

Multiple Choice

Find the measure of the missing angle.

• 90^o
• 10⁰
• 130^o
• 50^o

Multiple Choice

The line pictured has a(n) ______ slope.

• Positive
• Negative
• Undefined
• Zero

Multiple Choice

The Triangle Sum Theorem states that the sum of all angles in a triangle is ______. 

• 45°
• 90°
• 180°
• 360°

Multiple Choice

The line pictured has a(n) ______ slope.

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

An angle that is exactly 90 degrees.

• right
• acute
• obtuse
• straight

Multiple Choice

What is the slope of the line? ( Make sure to simplify!!!! I might try to trick you hint.. hint.. hint)

• -6/2

• -3/1

• 1/3

• 2/6

Multiple Choice

An angle that is less than 90^o.

• right
• acute
• obtuse
• straight

Multiple Choice

What is the slope of the line?

• 3/1

• -3/1

• 3

• -1/3

Multiple Choice

What is the value of x?

• 38

• 57

• 76

• 85

Multiple Choice

What is the slope?

• -21

• -17

• 5

• 4

Multiple Choice

Find the measure of the indicated angle. 

• 26
• 36
• 85
• 144

Multiple Choice

What is the slope?

• 5
• 1/5
• 15
• 10

Multiple Choice

Find the measure of the indicated angle.

• 95

• 85

• 35

• 45

Multiple Choice

What is the slope between the two points?

( 4, - 3 ) and ( 9, 2 )

• 1

• -1

• 5

• -5