What is the angle of the rotation from rst to r's't'

-90 degrees

Step-by-step explanation:

Draw a segment from the origin, point O, to point R. Draw a segment from the origin, point O, to point R'. The angle of rotation is the angle between segments OR and OR'.

The slope of segment OR is 2/3.

The slope of segment OR' is -3/2.

The slopes are negative reciprocals, so the segments are perpendicular.

The angle between the segments is 90 degrees. The rotation is counterclockwise, so it is a negative number of degrees.

The angle of rotation is -90 degrees.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.