Exploring Dilations and Scale Factor

The video tutorial begins with a review of the slope formula, followed by an introduction to the concept of dilations in geometry. It explains how to find scale factors and discusses the properties of dilations, such as preserving angle measures, betweenness, collinearity, and orientation. The tutorial also covers how to identify dilations versus reflections and how to use dilation rules, including handling fractions in calculations. The session concludes with practice exercises and a brief exit ticket.

What is the formula for calculating the slope between two points?

• (y2 - y1) * (x2 - x1)

• y2 + y1 / x2 + x1

• y2 - y1 / x2 - x1

• y1 - y2 / x1 - x2

What does the prime notation (') in geometry usually indicate?

• The new image after transformation

• The original figure before transformation

• The midpoint of the line segment

• The perpendicular bisector of the line

What is the scale factor if the original point (3,1) transforms to (6,2)?

• 2

• 3

• 0.5

• 1.5

What is the scale factor when the original figure is scaled down to a smaller size in a dilation?

• Zero

• A whole number greater than 1

• One

• A fraction less than 1

Which of the following is NOT a property of dilations?

• Preserves orientation

• Changes the angle measures

• Preserves collinearity

• Preserves betweenness

How do you determine if a transformation is a dilation?

• The shape flips over a line

• The shape increases or decreases uniformly

• The shape translates in a straight line

• The shape rotates around a point

Which transformation does not preserve the orientation of the shape?

• Reflection

• Dilation

• Rotation

• Translation

What should you use instead of decimals to avoid rounding errors in scale calculations?

• Scientific notation

• Percentages

• Exact fractions

• Whole numbers

If a point on a pre-image is at (1, -4) and the scale factor is 1.5, what is the new y-coordinate after dilation?

• -6

• -2

• 6

• 2

What is the correct interpretation of a scale factor of 1/3 in a dilation?

• The image is two-thirds smaller than the pre-image

• The image is three times smaller than the pre-image

• The image is three times the size of the pre-image

• The image is one-third the size of the pre-image