Exploring Math Transformations

In this video, Sean explains the four main types of geometric transformations: translations, reflections, rotations, and dilations. Translations involve sliding a figure without rotating it, ensuring the original and image are congruent. Reflections create a mirror image by flipping a figure over a line. Rotations turn a figure around a fixed point, maintaining congruency. Dilations resize a figure by a scale factor, resulting in a similar but not congruent image. Each transformation type is illustrated with examples and coordinate rules.

Which of the following is NOT one of the four main types of transformations?

• Scaling

• Reflection

• Translation

• Rotation

What is the main characteristic of a translation?

• The figure is flipped over a line.

• The figure is enlarged or reduced.

• The figure is turned around a fixed point.

• The figure is slid to another position without turning.

If a figure is translated by (x + 3, y - 2), what does '3' represent?

• Vertical units

• Rotation angle

• Horizontal units

• Scale factor

What happens to a figure when it is reflected over the y-axis?

• The x-coordinate becomes negative.

• The figure is rotated 90 degrees.

• The y-coordinate becomes negative.

• Both coordinates become negative.

To reflect a figure over the x-axis, which coordinate should be altered?

• x-coordinate

• Neither coordinate

• y-coordinate

• Both coordinates

What is the center of rotation?

• The point where a figure is dilated.

• The point where a figure is translated.

• The point where a figure is reflected.

• The point around which a figure is turned.

If a figure is rotated 90 degrees around a point, what happens to the figure?

• It is flipped over a line.

• It is slid to another position.

• It is enlarged or reduced.

• It is turned around a fixed point.

What does a scale factor of 1/2 do to a figure during dilation?

• Enlarges the figure

• Reduces the figure

• Flips the figure

• Slides the figure

If the scale factor is more than one, what happens to the figure?

• It is rotated.

• It is flipped.

• It is enlarged.

• It is reduced.

To get the coordinates of a dilated figure, what should you do?

• Subtract a constant from both coordinates.

• Add a constant to both coordinates.

• Divide both coordinates by the scale factor.

• Multiply both coordinates by the scale factor.