Reductions and Enlargements
What happens to the size of a figure when it is reduced?
The figure gets smaller while maintaining its shape and proportions.
What is dilation?
Dilation is a transformation that changes the size of a figure but keeps its shape and angles the same.
What is the main characteristic of similar figures?
They have the same shape but different sizes.
What is the term for a transformation that changes the size of a figure but not its shape?
Dilation.
A triangle with side lengths 4 cm, 5 cm, and 6 cm is reduced by a scale factor of 0.5. What are the new side lengths?
2 cm, 2.5 cm, and 3 cm.
If a figure is enlarged, how are the angles of the figure affected?
The angles remain the same; only the side lengths change proportionally.
What does it mean if a dilation has a scale factor greater than 1?
The figure is enlarged.
How are the corresponding angles of similar figures related?
The corresponding angles are congruent.
What do we call the ratio of the side lengths in a dilation?
Scale factor.
A square has side lengths of 3 units. If the scale factor of dilation is 4, what is the new perimeter of the square?
48 units. (New side length = 3 × 4 = 12 units, perimeter = 12 × 4 = 48 units). The model is a smaller version of the actual object, with all dimensions proportional.
What is the scale factor if the side lengths of a figure are reduced by half?
The scale factor is 0.5.
If a dilation has a scale factor less than 1, what happens to the figure?
The figure is reduced in size.
If two triangles are similar, how are their corresponding side lengths related?
Their side lengths are proportional.
Define "similar figures."
Figures that have the same shape but are different in size.
True or False: Dilation can occur in photography when zooming in or out on an image.
True.
True or False: Enlargements and reductions result in congruent figures.
False. They result in similar figures, not congruent figures.
How is the center of dilation used in a transformation?
It is the fixed point from which the figure is enlarged or reduced.
True or False: All congruent figures are similar, but not all similar figures are congruent.
True.
What is a reduction?
A transformation that decreases the size of a figure while keeping its shape and proportions.
The coordinates of point B are (3, 4). If point B is dilated with a scale factor of 0.75 from the origin, what are the new coordinates?
(2.25, 3)
If a figure with a side length of 4 units is enlarged by a scale factor of 3, what will be the new side length?
12 units
Find the coordinates of a point after dilation: If point A is (2, 3) and the scale factor is 2, what are the new coordinates of A'?
A'(4, 6).
Two rectangles are similar, and the side lengths of one are 3 cm and 6 cm. If the scale factor between the rectangles is 2, what are the side lengths of the other rectangle?
6 cm and 12 cm.
What is an enlargement?
A transformation that increases the size of a figure while keeping its shape and proportions.
If a blueprint uses a scale of 1:100, how long is a 3-meter wall in the blueprint?
3 centimeters.