Understanding Dilations and Their Properties

The video explores how the properties of shapes change under dilation. It examines whether coordinates, line segments, angle measures, side lengths, perimeter, and area are preserved. The video demonstrates that while angle measures are preserved, coordinates, side lengths, perimeter, and area are not. It also discusses the effects of dilation when centered at a vertex, showing that some line segments remain on the same line while others do not.

What happens to the coordinates of the vertices after a dilation?

• They become negative.

• They double in value.

• They change to new coordinates.

• They remain unchanged.

When a line segment is dilated, under what condition does it remain on the same line?

• If the dilation center is on the segment.

• If the segment is horizontal.

• If the segment is vertical.

• If the segment is parallel to the x-axis.

Are angle measures preserved during a dilation?

• Only if the center of dilation is at the origin.

• Only if the dilation is uniform.

• No, they are never preserved.

• Yes, they are always preserved.

What happens to the side lengths of a shape when it is dilated?

• They remain the same.

• They increase or decrease depending on the dilation.

• They become zero.

• They become infinite.

How does dilation affect the perimeter of a shape?

• The perimeter remains constant.

• The perimeter increases or decreases with dilation.

• The perimeter becomes zero.

• The perimeter doubles.

What is the effect of dilation on the area of a shape?

• The area becomes infinite.

• The area remains unchanged.

• The area becomes zero.

• The area increases or decreases with dilation.

In a vertex-centered dilation, which vertex remains unchanged?

• The vertex at the center of dilation.

• The vertex with the smallest coordinate.

• The vertex opposite to the center.

• The vertex with the largest coordinate.

During a vertex-centered dilation, which line segments remain on the same line?

• Segments not passing through the center.

• No segments.

• Segments passing through the center.

• All segments.

What happens to the side lengths in a vertex-centered dilation?

• They become zero.

• They increase or decrease depending on the dilation.

• They remain unchanged.

• They become infinite.

How does a vertex-centered dilation affect the area of a shape?

• The area becomes infinite.

• The area becomes zero.

• The area increases or decreases with dilation.

• The area remains constant.