Mystery Questions
Graphs and More
Scale Factor
Identifying Scale Factor
Mixed
100
Segment YZ measures 3 units.
What is the length, in units, of the image of segment YZ after a dilation using a scale factor of 2?
6 units
100
Dilate by a scale factor of 2, then graph both the pre-image and image
Pre-Image
L: (3, 5)
M: (7, 8)
Image coordinates:
L' (6, 10)
M' (14, 16)
100
The coordinates for point A are (11, 15). After using a scale factor of 2, what would the new coordinates be for A'?
A': (22, 30)
100
What is the scale factor? Pre-image on left, Image on the right
Scale Factor is 3
100
True or False.
The triangle on the left was dilated by a scale factor of 1/2 to become the triangle on the right
True
When the scale factor is a fraction, we divide
200
If side AB has a measure of 14 miles, and was dilated by a scale factor of 12, what is the new measurement?
New measurement of A'B': 168 miles
200
Dilate by a scale factor of 1/2, then graph both the pre-image and image
Pre-Image
L: (3, 5)
M: (7, 8)
Image Coordinates:
L' (1.5, 2.5)
M' (3.5, 4)
200
If C' is (25, 35) and the scale factor was 5. What is C?
C (5, 7)
Scale Factor multiples to both x and y making 5 turn into 25, and 7 into 35
200
The point (2, 5) was dilated to become point (8,20). What was the scale factor?
Scale Factor is 4
200
Dilate the point (93, 210) by a scale factor of 1/3
New point: (31, 70)
300
What is the scale factor?
A (4, 6)
A' (32, 48)
Scale Factor is 8
300
Dilate by a scale factor of 1/3, then graph both the pre-image and image
Pre-Image
E: (12, 15)
F: (3, 9)
Image coordinates
E' (4, 5)
F' (1, 3)
300
Point A is (22, 34). If we dilate by a scale factor of 1/3, what is Point A's new coordinates?
Answer must be written as a mixed number
A' (7 1/3 , 11 1/3)
Divide both x and y by 3
300
If x is 20, what is the Scale Factor?
Scale Factor would be 4
300
Triangle ABC will be dilated by a scale factor of 1/2. What will be the coordinates of A'?
(-1,-2.5)
400
True or false:
Dilations are rigid transformations.
False
Dilations are non-rigid. Rigid transformations keep the same size as the pre-image. Dilations do not keep the same size
400
Dilate by a scale factor of 8.5. List the coordinates of the image.
S (8, -5)
T (-12, -1)
U (11, 10)
Image Coordinates:
S' (68, -42.5)
T' (-102, -8.5)
U' (93.5, 85)
400
Point A (18, 43)
Point B (53, 43)
Point C (18, 53)
Find A', B', C' after dilating by a Scale Factor of 1/2
A' (9, 22.5)
B' (26.5, 22.5)
C' (9, 26.5)
Divide each point by 2
400
Pre-image point (3, 5)
Image point (10.5, 17.5)
What was the scale factor?
Scale Factor is 3.5
We multiplied both the x and y coordinate by 3.5
400
What would be the new coordinate point if (13, 12) was dilated by a scale factor of 3.5?
New point: (45.5, 42)
Multiple each coordinate by 3.5
500
Select all true statements.
A. Dilations always increase the length of line segments.
B. When a figure is dilated, the image and the pre-image are the same size and shape.
C. When a figure is dilated, the angle measures in the image are greater than the corresponding angle measures of the original figure.
D. Dilations of a figure are always the same size to the original figure.
E. Dilations of a figure are the same shape to the original figure.
Only E
Dilations do not keep the same size. The geometric shape is the same both for the image and pre-image of a dilation
Example: triangle dilates to become a larger or smaller triangle. Line segment becomes longer or shorter. Both are still the same shape as they started
500
Dilate the figure by a scale factor of 3.5. What are the coordinates of the Image?
X (4, 5) Y (6, 7) Z (8, 9)
X' (14, 17.5)
Y' (21, 24.5)
Z' (28, 31.5)
500
Dilate each point by a scale factor of 1/3
A (83, 69)
B (14, 69)
C (14, 83)
Answers must be written as a mixed number
A' (27 2/3, 23)
B' (4 2/3, 23)
C' (4 2/3, 27 2/3)
500
If we start with the pre-image point of (11, 28)
after we dilate, the image point is (27.5, 70).
What is the Scale Factor?
Scale Factor is 2.5
500
What is the new point if we dilate (-6, 9) by a scale factor of 6.5?
New point: (-39, 58.5)