Rotating Points and Quadrants

Front

What are the four quadrants in a Cartesian coordinate system?

Back

Quadrant I: (+, +), Quadrant II: (-, +), Quadrant III: (-, -), Quadrant IV: (+, -)

Front

How do you determine the quadrant of a point (x, y)?

Back

If x > 0 and y > 0, it's in Quadrant I; if x < 0 and y > 0, it's in Quadrant II; if x < 0 and y < 0, it's in Quadrant III; if x > 0 and y < 0, it's in Quadrant IV.

Front

What is the rule for rotating a point 90 degrees counterclockwise around the origin?

Back

(x, y) -> (-y, x)

Front

What is the rule for rotating a point 90 degrees clockwise around the origin?

Back

(x, y) -> (y, -x)

Front

What is the rule for rotating a point 180 degrees around the origin?

Back

(x, y) -> (-x, -y)

Front

If a point (a, b) is rotated 90 degrees counterclockwise, what will be its new coordinates?

Back

(-b, a)

Front

If a point (a, b) is rotated 90 degrees clockwise, what will be its new coordinates?

Back

(b, -a)

Front

What happens to the coordinates of a point when it is rotated 180 degrees?

Back

The coordinates change from (x, y) to (-x, -y).

Front

What is the effect of rotating a point around the origin?

Back

The point's position changes based on the angle of rotation, but its distance from the origin remains the same.

Front

How do you identify the new position of a triangle after a rotation?

Back

By applying the rotation rules to each vertex of the triangle.