Dilations, Similarity, and Introducing Slope

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 center of dilation and a scale factor.

Front

What does a scale factor of 1/2 mean in dilation?

Back

A scale factor of 1/2 means that the image will be half the size of the original figure.

Front

How do you determine if two figures are similar?

Back

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

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points are expanded or contracted.

Front

If a point (x, y) is dilated by a scale factor of k, what is the new coordinate?

Back

The new coordinate will be (kx, ky).

Front

What is the relationship between the dimensions of similar figures?

Back

The dimensions of similar figures are proportional to each other based on the scale factor.

Front

What is the scale factor used to create rectangle B from rectangle A if A has dimensions 10 by 5 and B has dimensions 15 by 7.5?

Back

The scale factor is 3/2.

Front

If point F at (7, 6) is dilated by a scale factor of 1/2, what is the new coordinate?

Back

The new coordinate F' is (3.5, 3).

Front

What does it mean for two shapes to be dilated from the same center?

Back

It means that both shapes are resized using the same fixed point, maintaining their relative positions.

Front

How can you find the image of a point after dilation?

Back

Multiply the coordinates of the original point by the scale factor.