Transformations GEO TEST 24-25

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a specified angle in a specified direction.

Front

What are the coordinates of a point after a 180-degree rotation around the origin?

Back

If a point A(x, y) is rotated 180 degrees around the origin, the new coordinates A' will be (-x, -y).

Front

If a point is in Quadrant I, where will it be after a 180-degree rotation?

Back

After a 180-degree rotation, a point in Quadrant I will move to Quadrant III.

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in the same direction.

Front

How do you find the translation vector from point A(x1, y1) to A'(x2, y2)?

Back

The translation vector can be found by subtracting the coordinates: .

Front

What happens to the coordinates of a point when it is reflected over the line y = x?

Back

When a point A(x, y) is reflected over the line y = x, the new coordinates A' will be (y, x).

Front

What is the effect of reflecting a point over the x-axis?

Back

Reflecting a point A(x, y) over the x-axis results in the new coordinates A'(-x, y).

Front

What is the effect of reflecting a point over the y-axis?

Back

Reflecting a point A(x, y) over the y-axis results in the new coordinates A'(-x, -y).

Front

If A(20, 30) and A'(25, 50), what is the translation vector?

Back

The translation vector is <5, 20>.

Front

What is the formula for a 90-degree rotation counterclockwise around the origin?

Back

For a 90-degree counterclockwise rotation, the new coordinates A'(x, y) will be (-y, x).