Exploring Geometric Transformations: Translation, Reflection, Dilation, and Rotation

The video tutorial covers four types of geometric transformations: translation, reflection, dilation, and rotation. It explains how translation involves moving a figure without changing its size or orientation, ensuring congruence between the original and translated figures. Reflection is described as creating a mirror image across a line, with examples of reflections over vertical, horizontal, and diagonal lines. Dilation involves enlarging or reducing a figure with respect to a center point, using a scale factor. The tutorial provides examples and calculations for each transformation type.

What is a transformation in which a geometric figure is moved to another location without any change in size or orientation?

• Reflection

• Dilation

• Translation

• Rotation

In a translation, what is true about the original figure and its image?

• They are different in size

• They are similar

• They are rotated

• They are congruent

If a point A with coordinates (3, 4) is translated 6 units left and 6 units down, what are the new coordinates of A?

• (-3, 4)

• (3, -2)

• (-3, -2)

• (9, 10)

What is the line called across which a geometric figure is reflected to create a mirror image?

• Axis of rotation

• Line of reflection

• Line of symmetry

• Center of dilation

When reflecting a point over the x-axis, what happens to the coordinates?

• Neither coordinate changes

• The x-coordinate changes sign

• Both coordinates change sign

• The y-coordinate changes sign

When reflecting a point over the y-axis, what happens to the coordinates?

• Neither coordinate changes

• Both coordinates change sign

• The y-coordinate changes sign

• The x-coordinate changes sign

What is a transformation in which a figure is enlarged or reduced with respect to a point called?

• Rotation

• Reflection

• Dilation

• Translation

In a dilation, what is the point called with respect to which the figure is enlarged or reduced?

• Center of rotation

• Line of reflection

• Center of dilation

• Axis of symmetry

If a figure is dilated with a scale factor of 2, what happens to the length of its sides?

• They are tripled

• They are doubled

• They remain the same

• They are halved

What is the result of translating a triangle 4 units left and 5 units down?

• The triangle is enlarged

• The triangle is moved without changing its size or orientation

• The triangle is reflected

• The triangle is rotated