Adding and Subtracting Rational Expressions

The video tutorial covers the concept of transformations, focusing on dilations. It explains the role of scale factors and centers of dilation, differentiating between enlargement and reduction. Practical examples demonstrate how to apply dilations to geometric figures, and methods for calculating scale factors are discussed. The tutorial concludes with a section on the composition of transformations, illustrating how multiple transformations can be combined.

What is a dilation in the context of transformations?

• A transformation that produces a congruent figure

• A transformation that produces a similar figure

• A transformation that only translates the figure

• A transformation that changes the shape of the figure

What is the scale factor of an enlargement?

• Equal to 1

• Between 0 and 1

• Less than 1

• Greater than 1

What does a reduction in dilation result in?

• An image larger than the preimage

• An image smaller than the preimage

• An image of the same size as the preimage

• A different shape than the preimage

If the center of dilation is the origin and the scale factor is 2, what are the new coordinates of point A(-2, 3)?

• (-4, 3)

• (-4, 6)

• (-2, 6)

• (-1, 1.5)

What is the new coordinate of point B(3, 5) after a dilation with a scale factor of 2 centered at the origin?

• (6, 10)

• (1.5, 2.5)

• (6, 5)

• (3, 10)

What is the result of multiplying the coordinates of a point by 1/2 in a dilation?

• The point remains unchanged

• The point changes direction

• The point moves closer to the origin

• The point moves further from the origin

If the original side length of a figure is 4 units and the new side length after dilation is 10 units, what is the scale factor?

• 4

• 0.4

• 2.5

• 10

What is the center of dilation if the figure zooms out from point P(-1, -1)?

• (1, 1)

• (-1, -1)

• (0, 0)

• (-2, -2)

What is the result of translating a point (2, 3) by the vector (2, 1)?

• (4, 4)

• (0, 2)

• (2, 4)

• (4, 3)

What is the final coordinate of point X(-1, 2) after translating by (2, 1) and then dilating by a scale factor of 2?

• (1, 5)

• (2, 4)

• (0, 3)

• (2, 6)