Understanding Transformations from Coordinates

The video tutorial covers identifying geometric transformations from coordinates, including dilations, translations, reflections, and rotations. It explains how to recognize each transformation type by analyzing patterns in coordinate changes, such as multiplication for dilations, addition or subtraction for translations, sign changes for reflections, and coordinate swapping for rotations. The tutorial also provides examples to illustrate these concepts and help viewers apply the rules to identify transformations.

What is the algebraic rule for a dilation if the scale factor is 3?

• x + 3, y + 3

• 3x, 3y

• x - 3, y - 3

• 3x, y

How can you identify a translation from a set of coordinates?

• Look for swapped positions of coordinates

• Look for addition or subtraction patterns

• Look for sign changes in one coordinate

• Look for multiplication patterns

What happens to the coordinates during a reflection over the x-axis?

• The y-coordinate changes sign

• Coordinates are swapped

• Both coordinates change signs

• The x-coordinate changes sign

Which of the following indicates a rotation transformation?

• Only one coordinate changes sign

• Coordinates are added or subtracted by a constant

• Coordinates are swapped and one sign changes

• Both coordinates are multiplied by a scale factor

If a point (2, 3) is rotated 180 degrees about the origin, what will be the new coordinates?

• (2, -3)

• (3, 2)

• (-3, -2)

• (-2, -3)

In the example of a dilation, what is the scale factor if the original point is (3, 4) and the new point is (6, 8)?

• 4

• 3

• 2

• 1/2

What is the rule for a translation if a point moves from (0, 4) to (2, 3)?

• x - 2, y + 1

• x + 1, y + 2

• x + 2, y - 1

• x - 1, y - 2

How do you confirm a dilation transformation?

• Check for swapped coordinates

• Check for a consistent scale factor

• Check for sign changes

• Check for addition patterns

What is the rule for a reflection if only the y-coordinates change signs?

• x, y

• -x, -y

• -x, y

• x, -y

In a translation, if the x-coordinates increase by 10, what is the transformation rule?

• x + 10, y

• x, y + 10

• x - 10, y

• x, y - 10