Exploring Transformations in Algebra

The video tutorial covers various geometric transformations, including reflections, translations, rotations, and dilations. It explains each transformation's algebraic rules and demonstrates how to apply them to figures on a graph. The tutorial also includes methods for identifying transformations based on given figures.

What happens to the y-coordinate of a point when it is reflected over the x-axis?

• It stays the same.

• It becomes the opposite value.

• It is divided by two.

• It doubles.

In a reflection over the y-axis, what happens to the x-coordinate of a point?

• It becomes the opposite value.

• It stays the same.

• It doubles.

• It is divided by two.

When translating a figure 2 units to the right and 5 units down, what is the algebraic rule?

• (x - 2, y + 5)

• (x + 2, y + 5)

• (x - 2, y - 5)

• (x + 2, y - 5)

What is the result of translating a point (3, 4) by the rule (x - 3, y + 2)?

• (0, 6)

• (6, 2)

• (0, 2)

• (6, 6)

What is the algebraic rule for a 90-degree counterclockwise rotation?

• (x, y) -> (-x, -y)

• (x, y) -> (-y, x)

• (x, y) -> (y, -x)

• (x, y) -> (x, -y)

After a 180-degree rotation, what happens to the coordinates of a point (x, y)?

• (x, y) -> (-y, x)

• (x, y) -> (-x, -y)

• (x, y) -> (y, -x)

• (x, y) -> (x, -y)

What is the effect of a dilation with a scale factor greater than 1?

• The figure gets smaller.

• The figure stays the same size.

• The figure gets larger.

• The figure flips.

If a figure is dilated by a scale factor of 0.5, what happens to its size?

• It stays the same size.

• It gets half as large.

• It flips.

• It doubles in size.

How can you identify a 90-degree counterclockwise rotation from a figure?

• The figure is flipped over the x-axis.

• The x and y coordinates are swapped, and the new y-coordinate is the opposite of the original x-coordinate.

• The coordinates of the points are doubled.

• The figure is translated to the right.

What transformation has occurred if the coordinates of a point change from (3, 5) to (-3, 5)?

• 90-degree rotation

• Translation

• Reflection over the y-axis

• Reflection over the x-axis