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.

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.

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).

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).

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.

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).

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.

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.

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).

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).