Question

Which sequence of transformations will change figure PQRS to figure P′Q′R′S′?

Answer 1

To find the answer, we need to find the coordinate of figure PQRS, but I will only find the coordinate of point P which is:
P(1,-3), and the coordinates of P'(-3,1)
First choice:
Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis
Counterclockwise rotation 90° means that rotate 270° clockwise, and the formulaa to find it is
270° Rotation
(x,y) to (-y,x)
Point P rotate 270° counterclockwise
(1,-3) to (3,1)
Reflection over x-axis formula is
(x,y) to (x,-y)
Do the same to point P
(3,1) to (3,-1) which is not right because the coordinate of point P is (-3,1) not (3,-1)
Just to save times
Let check the last one
Counterclockwise rotation about the origin by 90 degrees followed by reflection about the y-axis
We already have the coordinate of rotate 90° counterclockwise which is
(3,1)
Then, reflection over y-axis formula is
(x,y) to (-x,y), so
Point P'
(3,1) to(-3,1) which is right. As a result, Counterclockwise rotation about the origin by 90 degrees followed by reflection about the y-axis is your final answer. Hope it help!