Math 2 Final Exam Review: Unit 1

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape. Common transformations include translations, rotations, reflections, and dilations.

Front

Define x-axis reflection.

Back

X-axis reflection is a transformation that flips a figure over the x-axis, changing the sign of the y-coordinates of the points in the figure.

Front

What is a dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but maintains its shape. It is defined by a scale factor, which determines how much the figure is enlarged or reduced.

Front

What does a scale factor of 0.5 indicate in dilation?

Back

A scale factor of 0.5 indicates that the figure is being reduced to half its original size.

Front

What is the effect of a 180° rotation on a point (x, y)?

Back

A 180° rotation around the origin transforms the point (x, y) to (-x, -y).

Front

Explain the transformation sequence: reflect across the y=x line, translate down 7 units, rotate 180° clockwise.

Back

1) Reflecting across the line y=x swaps the coordinates (x, y) to (y, x). 2) Translating down 7 units subtracts 7 from the y-coordinate. 3) Rotating 180° clockwise changes (x, y) to (-x, -y).

Front

What is the result of a 90° counter-clockwise rotation on a point (x, y)?

Back

A 90° counter-clockwise rotation around the origin transforms the point (x, y) to (-y, x).

Front

Define the term 'pre-image' in geometry.

Back

The pre-image is the original figure before any transformations are applied.

Front

What is the difference between a translation and a reflection?

Back

A translation moves a figure from one location to another without changing its shape or orientation, while a reflection flips a figure over a line, creating a mirror image.

Front

What does it mean to rotate a figure 270° counter-clockwise?

Back

Rotating a figure 270° counter-clockwise is equivalent to rotating it 90° clockwise. It changes the position of the points in a circular manner around a center point.