Dilation and Transformation Concepts

The video tutorial covers the concept of dilations in geometry, starting with an introduction to the basic principles and terminology. It includes exercises and examples to illustrate dilations, both as enlargements and reductions. The tutorial also explains scalar multiplication and its application in dilations, followed by composite transformations that involve dilations. The video concludes with examples of transformations on the coordinate plane, emphasizing the importance of the center of dilation.

What is the first step in dilating triangle ABC about point P?

• Reflect the triangle over the x-axis.

• Move point P to the center of the triangle.

• Draw rays from point P through each vertex of the triangle.

• Draw lines parallel to the sides of the triangle.

What happens to the image when the center of dilation, P, is moved?

• The image becomes a mirror reflection.

• The position of the image changes.

• The image rotates around the origin.

• The image remains unchanged.

When using scalar multiplication on the coordinate plane, where is the center of dilation typically located?

• At the intersection of the x and y axes.

• At one of the vertices of the pre-image.

• At the midpoint of the pre-image.

• At the origin.

In the exercise with a scale factor of 2/5, what type of transformation is being performed?

• Translation

• Enlargement

• Reduction

• Rotation

What is the scale factor used in the enlargement exercise?

• 2/5

• 3/2

• 1/2

• 2/3

What is the result of multiplying each element in the pre-image matrix by a scalar greater than one?

• The image is rotated.

• The image is translated.

• The image is reduced.

• The image is enlarged.

In a composite transformation, what is the first step when using a glide transformation?

• Rotate the figure 90 degrees.

• Slide the figure over by adding to the x and y coordinates.

• Dilate the figure with a scale factor of 2.

• Reflect the figure over the y-axis.

What is unique about the dilation in the final example?

• The center of dilation is at the origin.

• The center of dilation is not at the origin.

• The scale factor is less than one.

• The dilation is combined with a reflection.