Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a scale factor.

Tags

CCSS.8.G.A.3

Front

What does the scale factor indicate in a dilation?

Back

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

Tags

CCSS.8.G.A.3

Front

If a triangle has vertices at (2, 3), (4, 5), and (6, 7), what are the coordinates after a dilation with a scale factor of 1/2?

Back

The new coordinates will be (1, 1.5), (2, 2.5), and (3, 3.5).

Tags

CCSS.8.G.A.3

Front

What is the rule for dilating a point (x, y) by a scale factor of 3?

Back

The rule is (x, y) → (3x, 3y).

Tags

CCSS.8.G.A.3

Front

How do you determine if a dilation is an enlargement or a reduction?

Back

If the scale factor is greater than 1, it is an enlargement. If the scale factor is between 0 and 1, it is a reduction.

Tags

CCSS.8.G.A.3

Front

What are the coordinates of point C' if point C is at (1, 2) and the scale factor is 2?

Back

The coordinates of C' will be (2, 4).

Tags

CCSS.8.G.A.3

Front

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

Back

A scale factor of 1 means the figure remains the same size; it does not change.

Tags

CCSS.8.G.A.3

Front

If triangle ABC is dilated by a scale factor of 1/3, what happens to its area?

Back

The area of triangle ABC will be reduced to 1/9 of its original area.

Tags

CCSS.8.G.A.3

Front

What is the formula for dilating a point (x, y) by a scale factor of k?

Back

The formula is (x, y) → (kx, ky).

Tags

CCSS.8.G.A.3

Front

If a triangle is dilated and the new coordinates are (6, 8), what could be the original coordinates if the scale factor is 2?

Back

The original coordinates could be (3, 4).

Tags

CCSS.8.G.A.3