Transformations
Proportions
Scale Factor
Similar Figures
Find the New Coordinate
100
Which transformation moves a figure left, right, up, and down WITHOUT flipping or turning it?
Translation, Reflection, Rotation, or Dilation
Translation
100
Solve the proportion below:
x = 30
2x = 60
or 2 x 5 = 10 so 6 x 5 = 30
100
What was the scale factor used to get from Triangle A to Triangle B?
Scale Factor = 2
4 x 2 = 8
3 x 2 = 6
5 x 2 = 10
100
Find x.
x = 9
3/5 = x/15
5x = 45
or use scale factor of 3
100
The point (1, 2) is reflected over the x-axis. What is the new coordinate?
(1, 2) ---> (1, -2)
(x, y) ---> (x, -y)
200
Which transformation does the figure below represent?
Translation, Reflection, Rotation, or Dilation
Reflection
They are mirror images of each other!
The triangle is FLIPPED across the y-axis
200
Solve the proportion:
x = 3
20x = 60
or 4 x 5 = 20 so what times 5 is 15
200
What scale factor was used to get from Triangle 2 to Triangle 1?
Scale Factor = 4
Sides 2 and 8 line up
2 times what scale factor would make 8?
200
What is the height of the flagpole?
The flagpole is 51 feet tall.
200
The point (-2, 3) is rotated 90 degrees counterclockwise. What is the new coordinate?
(-2, 3) ---> (-3, -2)
(x, y) ---> (-y, x)
300
Which transformation (Translation, Reflection, Rotation, or Dilation) was applied to the figure below?
Rotation
The blue figure is TURNED 90 degrees clockwise.
300
x = 10
5(x - 4) = 30
5x - 20 = 30
5x = 50
300
A model of the Eiffel Tower is 2 feet tall. The actual Eiffel Tower is 984 feet tall. What is the scale factor that would be used to enlarge the model to the height of the actual Eiffel Tower?
Scale Factor = 492
2 times what is 984?
or actual height/model height = 984/2
300
Solve for x.
x = 4
3/6 = x/8
6x = 24
or scale factor is 1/2
300
The point (4, 5) is dilated by a scale factor of 4. What is the new coordinate?
(4, 5) ---> (16, 20)
(x, y) ---> (4x, 4y)
400
Translation, Reflection, Rotation, Dilation
Which transformation above does NOT give us a CONGRUENT figure?
Dilation
Dilations create SIMILAR figures.
Similar figures are the same shape, but the size changes!
400
Solve the proportion.
x = -3
4x = 2(x - 3)
4x = 2x - 6
2x = -6
400
What was the scale factor used to get from Triangle B to Triangle C?
Scale Factor = 1/3
12 x 1/3 = 4
15 x 1/3 = 5
9 x 1/3 = 3
400
Solve for x.
x = 7
3/4 = 9/x + 5
36 = 3(x + 5) = 3x + 15 ---> 3x = 21
or scale factor is 3
400
Reflect Point A across the y-axis using the rule: (x, y) ---> (-x, y). What is the new coordinate?
Point A is at (3, -2)
(x, y) ---> (-x, y)
(3, -2) ---> (-3, -2)
500
What transformations happen to get from Triangle ABC to Triangle A''B''C''?
Rotation and Reflection
The triangle is first ROTATED, then it is REFLECTED.
It TURNS 90 degrees counterclockwise, then is FLIPPED over the x-axis
500
Solve the proportion:
x = 9
5(x - 3) = 3(x + 1)
5x - 15 = 3x + 3
2x = 18
500
What was the scale factor applied to the blue triangle to produce the green triangle?
Scale Factor = 2
Short side blue = 2, Short side green = 4
Base blue = 3, Base green = 6
500
These triangles are similar. Solve for x.
x = 8
5x + 2/21 = 7x/28
140x + 56 = 147x
56 = 7x
500
Translate the point (7, 5) UP 3 units and to the LEFT 6 units.
(7, 5) ---> (7 - 6, 5 + 3) ---> (1, 8)
UP means to ADD to the Y-value
LEFT means to SUBTRACT from the X-value