Question

PQR has vertices P(-4,4),Q(-2,3), and R(-5,2). PQR is rotated 90° clockwise around the origin. Then the image is translated 5 units down and reflected across the y-axis. What are the coordinates of P"Q"R"? Show your work.

Answer 1

You have a figure with the following vertices:

P(-4,4)

Q(-2,3)

R(-5,2)

The figure is rotated 90° clockwise, then you use the following rule for such type of rotations:

(x,y) => (-y,x)

you apply the previous transformation for each vertex, just as follow:

P(-4,4) => P'(-4,-4)

y coordinate is now x coordinate but with opposite sign, and x coordinate is now the y coordinate. For the other points you have:

Q(-2,3) => Q'(-3,-2)

R(-5,2) => R'(-2,-5)

Next, the rotated figure is translated five units down. Here you only subtract 5 to y coordinates of all points

P'(-4,-4) => P''(-4,-8)

Q'(-3,-2) => Q''(-3,-6)

R'(-2,-5) => R''(-2,-10)

Finally, the figure is reflected across y axis, the rule for this is as follow:

(x,y) => (-x,y)

Hence, you obtain:

P''(-4,-8) => P'''(4,-8)

Q''(-3,-6) => Q'''(3,-6)

R''(-2,-10) => R'''(2,-10)