December 5, 2023

Which Graph Shows a Dilation?

In geometry, a dilation is a transformation that changes the size of a figure without changing its shape or orientation. A dilation can enlarge or reduce the figure by a specified amount, which is known as a scale factor. If the scale factor is greater than 1, the figure will be enlarged; otherwise, it will be reduced.

In order to perform a dilation, two pieces of information are needed: the center of dilation and the scale factor. The center of dilation can be any point on the coordinate plane, and the scale factor is a number that tells how much to enlarge or reduce the figure by. The following article will discuss which graph shows a dilation and how dilations are represented geometrically.

AABC has vertices A(6, 6), B(6, 6), and (-6, -2). Which graph shows the image of AABC after performing a dilation with scale factor 2 and center of dilation at point A?

The answer to this question is A, which shows a figure that has been dilated by a factor of 2. This dilation increases the lengths of all of the figures’ sides by a factor of 2, and it also changes the positions of all of the vertices. The dilated figure also maintains the same proportion between its corresponding angles in the original and dilated figures. The other graphs do not show a dilation because they change the shape of the figures. For example, the graph on the right shows a rotation of the square by 90 degrees, and the graph on the left shows a stretching of the square horizontally.


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