Unit 3 Review

Unit 3 Review

Translations, Rotations, Reflections, Oh my!

​Translations "Slide"

​Algebraic form: T_h,k(x,y)➜(x+h, y+k)

​

​To perform a translation, add the h value to the x value of your point (If h is negative subtract it), then add the k value to the y value of your point (If k is negative subtract it).

​

​Remember:

Horizontally (h) right is positive and left is negative

​Vertically (k) up is positive and down is negative.

Multiple Choice

Write the rule for this translation:

Slide 5 up and 7 right

• (x, y)---->(x + 5, y + 7)

• (x, y)-----> (x + 7, y + 5)

• (x, y)----> (x - 7, y + 5)

Multiple Choice

Determine how to translate triangle ABC to triangle A'B'C' ?

• (x + 2, y - 5)

• (x + 2, y - 9)

• (x - 2, y - 9)

• (x - 2, y + 9)

​Reflection "Flip"

​Remember our four rules for reflections:

​

• ​r_x-axis(x, y) ➜ (x, -y)

• ​​r_y-axis(x, y) ➜ (-x, y)

• ​​r_y=x(x, y) ➜ (y, x)

• ​​r_y=-x(x, y) ➜ (-y, -x)

​

​

Multiple Choice

What is the Algebraic Notation for this Reflection?

• (x, y) → (y, x)
• (x, y) → (-x, y)
• (x, y) → (-y, -x)
• (x, y) → (x, -y)

Multiple Choice

Reflect Point C over the y-axis:

• (-3, 2)
• (3,2)
• (-2,3)
• (3,0)

Multiple Choice

B(-2, -4)
Reflect over the line y = x

• (2, -4)
• (-4, 2)
• (-4, -2)
• (4, 2)

Multiple Choice

What is the rule for the following reflection? 

• Reflection across      x-axis
• Reflection across        y-axis
• Reflection across            y = x
• Reflection across          y = −x

​Rotations "Spin"

​Our rotation rules: ➜ °

​Counter clockwise(positive):

• R_90°(x, y)➜(-y, x)

• ​R_180°(x, y)➜(-x, -y)

• ​R_270°(x, y)➜(y, -x)

​

​Clockwise (Negative):

• ​R_-90°(x, y)➜(y, -x)

• ​R_-180°(x, y)➜(-x, -y)

• ​R_-270°(x, y)➜(-y, x)

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

Rotate the point (-3,-4) around the origin 180 degrees clockwise. State the image of the point.

• (-4,-3)
• (-4,3)
• (4,-3)
• (3,4)

Multiple Choice

Rotate the point (-5,8) around the origin 90 degrees clockwise. State the image of the point.

• (-8,5)

• (8,-5)

• (8,5)

• (5,-8)

Multiple Choice

Triangle C is rotated 180° 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

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

• A
• B
• C
• D

​Symmetry

​Two kinds of symmetry:

• ​Line Symmetry: Reflection that maps a figure to itself.

• ​Rotational Symmetry: Rotation that maps a figure to itself.

​

​Smallest possible angle of rotational symmetry: 360/n

​(n is the number of sides of the polygon)

​Remember to test if smallest possible angle works. Keep testing all multiples of smallest possible angle until reaching 180 degrees.

Multiple Choice

How many lines of Symmetry does this hexagon have?

• 3
• 6
• 9
• 12

Multiple Choice

What are the angles of rotation for an octagon?

• multiples of 45
• multiples of 51.4
• multiples of 60
• multiples of 72

Multiple Choice

How many lines of symmetry does this shape have?

• 1
• 2
• 3
• 4

Multiple Select

Which of the following shapes show a line of symmetry? (Select all that Apply)

​Review: Equation of a line

​Remember:

​Parallel slopes are equal

​

​Perpendicular slopes are opposite reciprocals (Flip-Change).

​

​Steps to find line:

1. ​Find slope m

2. ​Plug into y = mx+b with given point (x, y) to solve for b

3. ​Plug m and b into y = mx +b

Multiple Choice

Two lines that are perpendicular lines have ...

• Slope that is opposite reciprocals

• No Slope

• Slope that is the same

• none of the above

Multiple Choice

Write the equation of a line PERPENDICULAR to the line y = 3x + 2 that passes through the point (9, -2)

• y = -1/3x - 5

• y = 3x-29

• y = 1/3x -5

• y = -1/3x +1