Dilations Exploration

When the image A'B'C'D' is [b]larger[/b] than the original figure ABCD (the preimage), the dilation is called an enlargement. [b]What is the scale factor for enlargements?[/b]

1 a negative number between 0 and 1 greater than 1

When the image A'B'C'D' is [b]smaller[/b] than the original figure ABCD (the preimage), the dilation is called a reduction. [b]What is the scale factor for reductions?[/b]

a negative number greater than 1 between 0 and 1 1

What is the [b]center of dilation[/b] on this graph?

Point E, or the origin (0, 0)

Set the [b]scale factor to 2[/b]. The ordered pairs of the preimage are A (2, 2), B (6, 2), C (5, 4), and D (3, 4). [br]What are the ordered pairs of the image A'B'C'D'? [b]How are those ordered pairs related to the scale factor?[/b]

A' (4, 4), B' (12, 4), C' (10, 8), D' (6, 8)[br]Multiply the coordinates of each original point by the scale factor to get the image point coordinates.[br]

Now [b]set the scale factor to 0.5[/b]. How are the coordinates of the ordered pairs of the image A'B'C'D' related to the original points this time?

Now the image points are found by multiplying the preimage coordinates by 0.5

[b]Note:[/b] Using the scale factor in this way to find the coordinates of image points works when the center of dilation is the [u]origin[/u] (0, 0).

Is a dilation an [b]isometry[/b]?

Yes, because the image and preimage are congruent. No, because the image and preimage are not congruent.

With dilations, are the image and preimage [b]similar figures[/b]?

Yes, because the corresponding angles are congruent and the corresponding sides are proportional. No, because the corresponding angles are not congruent and the corresponding sides are not proportional.

– jensbet, Lance Bledsoe

Information: Dilations Exploration