Question

1 what is the role of the center of dilation in a transformation?
a it acts as the fixed point from which all angles are enlarged
b it acts as the fixed point from which all distances are scaled
c it determines the orientation of the image
d it ensures angle measures congruent

2 a rectangle has vertices at (1, 2), (1, 5), (4, 5), and (4, 2). if the rectangle is dilated by a scale factor of 0.5 with the center of dilation at (0, 0), what are the coordinates of the new vertices?
a (0.5, 1), (0.5, 2.5), (2, 2.5), (2, 1)
b (0.5, 0.5), (1, 1), (2, 2), (2.5, 2.5)
c (1, 1), (1, 2.5), (4, 2.5), (4, 1)
d (2, 4), (2, 10), (8, 10), (8, 4)

3 what is the formula for dilating a point when the center of dilation is at the origin?
a (x, y) → (k + x, k + y)
b (x, y) → (kx, ky)
c (x, y) → (x^k, y^k)
d (x, y) → (x/k, y/k)

4 which statement best explains why all circles are similar?
a only circles that share the same center are similar
b all circles have equal circumference
c all circles can be mapped onto one another using dilations and translations
d only circles with the same radius are similar

5 a map is marked with 1 cm : 400 m. if a road measures 4.5 cm on the map, what is its actual length?
a 2100 m
b 1800 m
c 2200 m
d 1700 m

6 if a building is 100 meters tall and you want to create a scale drawing using a scale factor of 1:1, what will be the height of the building in the scale drawing?
a 8 meters
b 1 meters
c 12 meters
d 10 meters

7 what remains unchanged in a figure after a dilation?
a the area of the figure
b the position of the figure
c the size of the figure
d the shape and angle measures of the figure

Explanation:

Step1: Recall dilation concepts

Dilation is a transformation that changes the size of a figure. The center of dilation is the fixed point from which all distances are scaled.

Step2: Analyze each option

• Option a: Angles are not changed from the center of dilation. Angles remain congruent in dilation.
• Option b: Correct. The center of dilation is the fixed point from which all distances are scaled.
• Option c: The orientation of the image is not determined by the center of dilation.
• Option d: Angle measures remain congruent due to the properties of dilation, not because of the center's role in that specific way.

Answer:

b. It acts as the fixed point from which all distances are scaled.