Dilations

What is a dilation in geometry?

• A transformation that changes the size of a figure but not its shape, involving a scale factor and a center of dilation.

• A method to rotate a figure around a point.

• A process of reflecting a figure across a line.

• A technique to translate a figure to a different location.

What is the scale factor in a dilation?

• A number that describes how much a figure is enlarged or reduced during a dilation.

• A measurement of the angle in a geometric figure.

• The distance between two points in a coordinate plane.

• A constant value that does not change during transformations.

What is the relationship between the original figure and the dilated figure?

• The dilated figure is identical to the original figure in size and shape.

• The dilated figure is similar to the original figure, meaning they have the same shape but different sizes.

• The dilated figure is larger than the original figure but has a different shape.

• The dilated figure is smaller than the original figure and has a different shape.

If a figure is dilated by a scale factor of 1/2, what happens to its area?

• The area remains the same.

• The area is doubled.

• The area is reduced by a factor of (1/2)² = 1/4.

• The area is increased by a factor of 2.

What is the center of dilation?

• A fixed point in the plane about which all points are expanded or contracted during a dilation.

• The point where all lines of dilation intersect.

• The midpoint of the shape being dilated.

• The origin of the coordinate system.

How do you find the coordinates of a dilated point?

• Multiply the original coordinates by the scale factor.

• Add the scale factor to the original coordinates.

• Subtract the scale factor from the original coordinates.

• Divide the original coordinates by the scale factor.

What is a real-world example of dilation?

• Resizing an image or a photograph, where the image is enlarged or reduced while maintaining its proportions.

• Changing the color of an object in a photograph.

• Cropping a photograph to focus on a specific area.

• Adding a filter to enhance the image quality.

If a triangle has vertices at (2, 3), (4, 5), and (6, 1), what are the new coordinates after a dilation by a scale factor of 2?

• (4, 6), (8, 10), and (12, 2)

• (2, 3), (4, 5), and (6, 1)

• (6, 8), (10, 12), and (12, 4)

• (0, 0), (0, 0), and (0, 0)

How do you determine if two figures are similar?

• Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

• Two figures are similar if they have the same area.

• Two figures are similar if they are both triangles.

• Two figures are similar if they are congruent.

If a square has a side length of 4 and is dilated by a scale factor of 3, what is the new area?

• 36

• 64

• 144

• 81