Dilation & Scale Factor

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but maintains its shape, using a scale factor.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation. It can be greater than 1 (enlargement) or less than 1 (reduction).

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 less than 1, it is a reduction.

Front

What is the formula for calculating the scale factor?

Back

The formula for scale factor is \( \frac{new}{old} \).

Front

If a triangle has vertices at (2, 3), (4, 5), and (6, 7), what are the new 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 happens to the area of a figure when it is dilated by a scale factor of k?

Back

The area of the figure is multiplied by \( k^2 \).

Front

If a figure is dilated by a scale factor of 3, what is the relationship between the original and the new figure?

Back

The new figure is three times larger in each dimension compared to the original figure.

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; there is no change.

Front

How do you find the coordinates of a point after dilation?

Back

To find the new coordinates after dilation, multiply each coordinate of the original point by the scale factor.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but may differ in size, typically achieved through dilation.