Dilations on the Coordinate Plane (Handout & Homework)

Front

What is a dilation in the context of the coordinate plane?

Back

A dilation is a transformation that alters the size of a figure on the coordinate plane while maintaining its shape. It is defined by a scale factor and a center of dilation.

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How do you represent a dilation mathematically?

Back

Front

If a rectangle has a length of 10 units and is dilated by a scale factor of 2, what will be the new length?

Back

Front

What happens to the coordinates of a point (x, y) when it is dilated by a scale factor of 0.5?

Back

The new coordinates will be (0.5x, 0.5y), effectively reducing the distance from the origin.

Front

True or False: A dilation can change the orientation of a figure.

Back

False. A dilation does not change the orientation of a figure; it only changes its size.

Front

What is the effect of a scale factor of 1 on a figure during dilation?

Back

A scale factor of 1 means the figure remains the same size; there is no change.

Front

If a triangle is dilated by a scale factor of 1.5, what is the rule for this dilation?

Back

The rule for this dilation is @@(x, y) ightarrow (1.5x, 1.5y)@@.

Front

What is the relationship between the original length and the dilated length in a dilation?

Back

Front

If a figure is dilated by a scale factor of 3, what happens to its area?

Back