IM 8.2.3 Lesson: Dilations with No Grid

Drag the point C to the place on the ray whose distance from A is twice the distance from B to A.

Drag the point D to the place on the ray whose distance from A is half the distance from B to A.

Use this app to answer the questions below.

Dilate [math]B[/math] using a scale factor of 5 and [math]A[/math] as the center of dilation. Which point is its image?

Using [math]H[/math] as the center of dilation, dilate [math]G[/math] so that its image is [math]E[/math]. What scale factor did you use?

Using [math]H[/math] as the center of dilation, dilate [math]E[/math] so that its image is [math]G[/math]. What scale factor did you use?

To dilate [math]F[/math] so that its image is [math]B[/math], what point on the diagram can you use as a center?

Dilate [math]H[/math], using [math]A[/math] as the center and a scale factor of [math]\frac{1}{3}[/math]. Which point is its image?

Describe a dilation that uses a labeled point as its center and that would take [math]F[/math] to [math]H[/math].

Using [math]B[/math] as the center of dilation, dilate [math]H[/math] so that its image is itself. What scale factor did you use?

Dilate P using C as the center and a scale factor of 4. Follow the directions to perform the dilations in the applet.

Select the Dilate From Point tool.[br][icon]/images/ggb/toolbar/mode_dilatefrompoint.png[/icon][br][br]Click on the object to dilate, and then click the center of dilation.When the dialog box opens, enter the scale factor. [br][br]Fractions can be written with plain text, ex. 1/2.[br][br]Click [icon]/images/ggb/toolbar/mode_buttonaction.png[/icon][br][br]Use the Ray tool and the Distance tool to verify.

Dilate Q using C as the center and a scale factor of 1/2.

Draw a simple polygon.

Choose a point outside the polygon to use as the center of dilation. Label it [math]C[/math].[br][br]Using your center [math]C[/math] and the scale factor you were given, draw the image under the dilation of each vertex of the polygon, one at a time. Connect the dilated vertices to create the dilated polygon.[br][br]Draw a segment that connects each of the original vertices with its image. This will make your diagram look like a cool three-dimensional drawing of a box! If there's time, you can shade the sides of the box to make it look more realistic.

Compare your drawing to other people’s drawings. What is the same and what is different? How do the choices you made affect the final drawing? Was your dilated polygon closer to [math]C[/math] than to the original polygon, or farther away? How is that decided?

Here is line segment DE and its image D'E' under a dilation. Use a ruler to find and draw the center of dilation. Label it F.

What is the scale factor of the dilation?