Given the points A=(2,-3) and B=(-3,1),if they are transformed to the points A'(-2,-3) and B'(3,1) what transformation occurred?Rotation or reflection?If rotation name the degree and direction and if reflection,name the line of reflection.

No graph necessary.

didn't it reflect around the y axis (x=0)?

Will it be reflection over the origin or will it be rotation 180 degrees clockwise/anti clockwise

No I'm sorry I got confused.You are correct.Thank you.

To determine whether a rotation or reflection occurred, we can compare the coordinates of the original points (A and B) with their transformed points (A' and B').

Let's analyze the x-components of the coordinates:
- The x-coordinate of point A changed from 2 to -2.
- The x-coordinate of point B changed from -3 to 3.

Since both x-coordinates of the points were negated, it indicates that a reflection occurred. A reflection is a transformation that flips each point across a line.

To find the line of reflection, we can take any two corresponding points and find the perpendicular bisector of the line segment connecting them.

Let's take points A and A':
- The x-coordinate of these points changed by 4, while the y-coordinate remained the same.
- The midpoint of the line segment connecting them is (-0.5, -3).

Now let's take points B and B':
- The x-coordinate of these points also changed by 4, while the y-coordinate remained the same.
- The midpoint of the line segment connecting them is (0, 1).

We have two midpoints (-0.5, -3) and (0, 1). To find the line of reflection, we can find the equation of the line passing through these two points.

Using the midpoint formula, we can calculate the slope of the line:
m = (y2 - y1) / (x2 - x1) = (1 - (-3)) / (0 - (-0.5)) = 4 / (-0.5) = -8

The negative reciprocal of the slope gives us the slope of the perpendicular bisector, which is 1/8. Let's denote the midpoint (0, 1) as (x0, y0). The equation of the line of reflection is then given by:

y - y0 = (1/8)(x - x0)

Using the coordinates of the midpoint (0, 1), the equation becomes:
y - 1 = (1/8)(x - 0)

Simplifying, we get:
y - 1 = (1/8)x

Therefore, the line of reflection is:
y = (1/8)x + 1

In conclusion:
- The transformation that occurred is a reflection.
- The line of reflection is y = (1/8)x + 1.