Which Graph Shows A Dilation?
In geometry, a dilation is a transformation that changes the size of a figure, but not its shape. It can either enlarge or reduce the figure by a scale factor. The scale factor is a number that tells you how much the figure is being enlarged or shrunk. A scale factor of 2 means that the figure is being enlarged twice as large, while a scale factor of 0.5 means that the figure is being shrunk to half its size.
To determine which graph shows a dilation, look for a graph where the original figure and the transformed figure have the same shape but different sizes. For example, the following graph shows a dilation of a square with a scale factor of 2:
Original figure: (0, 0) (1, 0) (1, 1) (0, 1) Transformed figure: (0, 0) (2, 0) (2, 2) (0, 2) In this graph, the original square has side length 1, and the transformed square has side length 2. The two squares have the same shape, but the transformed square is twice as large as the original square.
The following graph does not show a dilation of a square:
Original figure: (0, 0) (1, 0) (1, 1) (0, 1) Transformed figure: (0, 0) (1, 0) (1, 1) (0, 1) In this graph, the original square has side length 1, and the transformed square also has side length 1. The two squares have the same size, but they have different shapes. The transformed square is rotated 90 degrees counterclockwise from the original square.
Questions related to Which Graph Shows A Dilation
Here are some questions that can be used to test students’ understanding of dilations:
- Which of the following graphs shows a dilation of a circle with a scale factor of 2?
- Which of the following graphs shows a dilation of a triangle with a scale factor of 0.5?
- What is the scale factor of the dilation that takes a square with side length 1 to a square with side length 2?
- What is the scale factor of the dilation that takes a triangle with side lengths 3, 4, and 5 to a triangle with side lengths 6, 8, and 10?
These questions can be used to assess students’ ability to identify dilations, calculate scale factors, and understand the effects of dilations on shapes.
