Transformational Geometry: Dilation Concepts

Tom Radicchio introduces dilations in transformational geometry, explaining the concept using triangle ABC and a scale factor. The video explores conjectures about similar figures and tests different scale factors, including negative ones, to understand their effects on dilations. Advanced techniques are demonstrated, emphasizing the importance of exploration and discovery in learning geometry.

What is the primary focus of the first video in the transformational geometry unit?

• Reflections

• Translations

• Dilations

• Rotations

In the context of dilations, what is the term used to describe figures that have the same shape but different sizes?

• Equivalent figures

• Identical figures

• Similar figures

• Congruent figures

What is a conjecture in the context of transformational geometry?

• An opinion based on observation

• An unproven hypothesis

• A proven theorem

• A mathematical formula

When a triangle is dilated about a point, what remains unchanged between the preimage and the image?

• Shape

• Position

• Size

• Color

What happens to the image of a triangle when the scale factor is set to 3?

• The image becomes smaller

• The image becomes larger

• The image remains the same size

• The image disappears

How does a scale factor of 0.5 affect the position of the preimage and image?

• The image is outside the preimage

• The image is inside the preimage

• The image is identical to the preimage

• The image overlaps the preimage

What is the effect of a scale factor of 1.5 when point P coincides with a vertex of the triangle?

• The image is identical to the preimage

• The image is larger than the preimage

• The image is smaller than the preimage

• The image and preimage overlap at one vertex

What is the result of using a negative scale factor in a dilation?

• The image is identical to the preimage

• The image is congruent and rotated 180 degrees

• The image is larger

• The image is smaller

What is the relationship between the preimage and image when the scale factor is negative one?

• They are similar

• They are congruent

• They are identical

• They are different

Why does a negative scale factor result in a 180-degree rotation?

• Because of the dilation point

• Because of the scale factor value

• Because of the negative sign

• Because of the positive sign