Question

1. a point (2,3) is rotated 90° counter - clockwise around the origin. its new coordinates are: mark only one oval. (-3,2) (3,-2) (-2,3) (2,-3) 41. rotating a figure 180° about the origin results in: mark only one oval. the same figure at a new location a figure flipped over a line a figure in the same position a point at (-x,-y) 42. which of the following is a rotation? mark only one oval. flipping a figure over the x - axis turning a figure around a fixed point sliding a figure 3 units to the right enlarging a figure

Explanation:

Step1: Recall 90 - degree counter - clockwise rotation rule

For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(-y,x)$.
For the point $(2,3)$, $x = 2$ and $y = 3$. Applying the rule, we get $(-3,2)$.

Step2: Recall 180 - degree rotation rule

For a 180 - degree rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$. This applies to all points of a figure, so rotating a figure 180 - degree about the origin results in a point at $(-x,-y)$ for each point $(x,y)$ of the original figure.

Step3: Recall the definition of rotation

Rotation is the transformation of turning a figure around a fixed point. Flipping a figure over the x - axis is a reflection, sliding a figure 3 units to the right is a translation, and enlarging a figure is a dilation.

Answer:

1. A. (-3,2)
2. D. A point at (-x,-y)
3. B. Turning a figure around a fixed point