Plane Transformation Quiz

What is the result of rotating a point 90 degrees clockwise about the origin?

• (y, x)

• (y, -x)

• (x, -y)

• (-y, x)

If the center of rotation is at point (2,3), what are the new coordinates after rotating point (4,5) 180 degrees?

• (3,2)

• (2,3)

• (6,8)

• (0,1)

Explain the difference between a clockwise and counterclockwise rotation.

• Clockwise rotation goes up, counterclockwise rotation goes down.

• Clockwise rotation goes to the left, counterclockwise rotation goes to the right.

• Clockwise rotation goes forward, counterclockwise rotation goes backward.

• Clockwise rotation goes to the right, counterclockwise rotation goes to the left.

How can you determine the direction of rotation when given the center and the point to be rotated?

• Draw a vector from the center to the point to be rotated. The direction of rotation is determined by the direction of this vector.

• Check the color of the point

• Measure the distance between the center and the point

• Count the number of vertices in the shape

What is the formula to rotate a point (x,y) about the origin by an angle θ?

• x' = x * sin(θ) + y * cos(θ) and y' = x * cos(θ) - y * sin(θ)

• x' = x * cos(θ) + y * sin(θ) and y' = x * sin(θ) - y * cos(θ)

• x' = x * sin(θ) - y * cos(θ) and y' = x * cos(θ) + y * sin(θ)

• x' = x * cos(θ) - y * sin(θ) and y' = x * sin(θ) + y * cos(θ)

If a point is rotated 270 degrees counterclockwise about the origin, what are the new coordinates?

• (-y, x)

• (y, -x)

• (-x, y)

• (x, -y)

Describe the process of rotating a point about a given center using a protractor.

• Use the protractor to draw a circle around the point without measuring the angle

• Rotate the protractor around the point until it aligns with the center

• Place the center of the protractor on the center of rotation, align the base line with the line connecting the center and the point, read the angle measurement, and determine the new position.

• Estimate the angle by eye without using the protractor

What is the angle of rotation if a point is rotated 45 degrees clockwise about the point (3,4)?

• 45 degrees

• 360 degrees

• 180 degrees

• 90 degrees

When rotating a point about the origin, how does the sign of the coordinates change based on the quadrant?

• 1st quadrant - No change, 2nd quadrant - x becomes negative, y remains positive, 3rd quadrant - Both x and y become negative, 4th quadrant - x remains positive, y becomes negative.

• 3rd quadrant - x remains positive, y remains positive

• 1st quadrant - x becomes negative, y remains positive

• 2nd quadrant - Both x and y become negative

If a point is rotated 90 degrees counterclockwise about the point (1,1), what are the new coordinates?

• (1+y-1, 1-(x-1)) or (y, 2-x)

• (2-y, x-2)

• (y, x)

• (x, y)