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Answer by math_tutor2020(3259)    (Show Source):
You can put this solution on YOUR website! Refer to this handy chart  (image source: OnlineMath4all.com) The chart tells us that P(8,1) rotates to Q(-1,8) We use the rule in the second row telling us (x,y) rotates to (-y,x) when doing a 90 degree counter-clockwise rotation. We swap the x and y coordinates, then make the first coordinate (after the swap) the opposite sign of what it was before. Now, we apply a reflection over the line y = x The rule is that any (x,y) point reflects to (y,x). The x and y coordinates swap. There are no sign changes here. Q(-1,8) reflects to R(8,-1) When applying a y axis reflection, we change the sign on the x coordinate but the y coordinate stays the same. In general, we go from (x,y) to (-x,y) Specifically, R(8,-1) reflects to S(-8,-1) Answer: (-8,-1) Diagram:  I used GeoGebra to make the diagram. Answer by ikleyn(50557)
You can put this solution on YOUR website! . Q is the rotation of P(8,1) counter clockwise through 90* about the origin O, i.e. OP=OQ and angle QOP=90*. R Is the reflection of Q in the line y=x. S is the reflection of R in the y-axis. Find the coordinates of S. ~~~~~~~~~~~~~
(1) Since Q is rotation of P(8,1) clockwise through 90 degrees about the origin,
Q has the coordinates Q = (-1,8).
(2) R is the reflection of Q in the line y = x;
Hence, R = (8,-1). <<<---=== it is enough to make a sketch to get it . . .
(3) S is reflection of R in y-axis;
hence, S = (-8,-1). ANSWER
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