Coordinate Transformations and Symmetry

The video tutorial introduces the concept of symmetry about the x-axis, y-axis, and origin using points on a coordinate plane. It explains how points can be symmetrical across these axes and provides examples to illustrate the concept. The tutorial also summarizes the rules for identifying symmetry based on the coordinates of points and demonstrates these rules with a practical example.

What happens to the coordinates of a point when it is reflected across the x-axis?

• Neither coordinate changes.

• The x-coordinate changes sign.

• The y-coordinate changes sign.

• Both coordinates change sign.

Which of the following is true for points with x-axis symmetry?

• Neither coordinate changes.

• Both coordinates are the same.

• Y-coordinates are opposites.

• X-coordinates are opposites.

When reflecting a point across the y-axis, which coordinate changes?

• The x-coordinate changes sign.

• Neither coordinate changes.

• The y-coordinate changes sign.

• Both coordinates change sign.

For y-axis symmetry, what is true about the coordinates of the points?

• Y-coordinates are opposites.

• Both coordinates are the same.

• X-coordinates are opposites.

• X-coordinates are the same.

How do the coordinates of a point change when reflected across the origin?

• Neither coordinate changes.

• The y-coordinate changes sign.

• The x-coordinate changes sign.

• Both coordinates change sign.

What is the result of reflecting a point across both the x-axis and y-axis?

• The point remains unchanged.

• The point is reflected across the origin.

• Only the x-coordinate changes.

• Only the y-coordinate changes.

What is the coordinate transformation for reflecting a point across the x-axis?

• No change in coordinates.

• Replace y with -y.

• Replace x with -x.

• Replace both x and y with their negatives.

In the example, what are the new coordinates after reflecting the point (-3, 5) across the y-axis?

• (-3, -5)

• (-3, 5)

• (3, -5)

• (3, 5)

After reflecting the point (-3, 5) across the origin, what are the new coordinates?

• (3, -5)

• (-3, -5)

• (3, 5)

• (-3, 5)

What is the effect of rotating a point 180 degrees about the origin?

• The point is reflected across the origin.

• The point is reflected across the x-axis.

• The point remains unchanged.

• The point is reflected across the y-axis.