SOLUTION: 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 th

Algebra.Com
Question 1182539: 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.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (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(52787)   (Show Source): 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

Solved.



RELATED QUESTIONS

what are the coordinates of R, the image p(1,3) under counter clockwise rotation 90... (answered by Edwin McCravy)
Points P,Q have coordinates (-2,-1) and (3,11) respectively. Find |OP|,|OQ| and |OP + OQ| (answered by MathLover1)
Please explain and solve this question. I am very confused and do not know how to graph... (answered by ewatrrr)
Here is the graph:... (answered by Theo)
Suppose w is a cube root of unity with w not equal to 1 suppose P and Q are the points (answered by ikleyn)
: Suppose w is a cube root of unity with w not equal to 1 suppose P and Q are the points... (answered by ikleyn)
Suppose w is a cube root of unity with w not equal to 1 suppose P and Q are the points on (answered by Alan3354,greenestamps)
OPQR is a quadrilateral. A, B, C and D are the midpoints of OP, PQ, QR and RO,... (answered by ikleyn)
In right triangle ABC, AC = BC and angle C = 90. Let P and Q be points on hypotenuse AB,... (answered by foofy)