Transformations and similarity unit test 8
1. True or False: A dilation always preserves orientation.
Answer: True. A dilation is a transformation that uniformly scales an object, either making it larger or smaller, while preserving its shape and orientation.
2. Which transformation would result in an object being reflected over the x-axis?
a) Translation
b) Rotation
c) Dilation
d) Reflection
Answer: d) Reflection
3. Which transformation would result in an object being rotated around a given point?
a) Translation
b) Rotation
c) Dilation
d) Reflection
Answer: b) Rotation
4. In a coordinate plane, the point P(2, -3) is translated 4 units to the right and 5 units up. What are the coordinates of the image point P'?
Answer: The new x-coordinate is 2 + 4 = 6 and the new y-coordinate is -3 + 5 = 2. Therefore, the coordinates of the image point P' are (6, 2).
5. Triangle ABC has vertices at A(-1, 2), B(3, 4), and C(0, 1). Triangle DEF has vertices at D(2, 5), E(6, 7), and F(1, 4). Determine if the two triangles are similar.
Answer: To determine if two triangles are similar, we need to compare their corresponding sides and angles. Since triangles ABC and DEF have the same shape and their corresponding sides are proportional, we can conclude that they are similar.
6. A square has an area of 25 square units. If the side length of the square is tripled, what will be the area of the new square?
Answer: The side length of the original square is √25 = 5 units. When the side length is tripled, the new side length will be 5 x 3 = 15 units. Therefore, the area of the new square will be 15^2 = 225 square units.
7. True or False: Dilations preserve angles.
Answer: False. Dilations preserve the shape and proportion of an object, but they do not preserve angles. The angles of the dilated object will change in size but maintain the same relative measure.
8. Which transformation would result in an object being enlarged or reduced by a specific scale factor?
a) Translation
b) Rotation
c) Dilation
d) Reflection
Answer: c) Dilation