Question

Which sequence of transformations will change figure PQRS to figure P′Q′R′S′?Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 90 degrees followed by reflection about the y-axis
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis

Answer 1

The first one is your answer. Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis.

Answer 2

Answer:  The correct option is

(A) Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis

Step-by-step explanation:  We are given to select the sequence of transformations that will change figure PQRS to figure P'Q'R'S'.

From the graph, we note that

the coordinates of the vertices of quadrilateral PQRS are P(-3, -2), Q(-2, -3), R(-3, -4) and S(-4, -4).

And, the co-ordinates of the vertices of quadrilateral P'Q'R'S' are P'(2, 3), Q'(3, 2), R'(4, 3) and S'(4, 4).

We see that

if a point (x, y) is rotated counterclockwise about the origin by 90 degrees and then reflected about the x-axis, its co-ordinates changes as follows :

$(x,y)~~~\Rightarrow~~~(-y,x)~~~\Rightarrow~~~(-y,-x).$

So with the same sequence of transformations, we see that

P(-3, -2)   ⇒   P'(2, 3),

Q(-2, -3)  ⇒   Q'(3, 2),

R(-3, -4)  ⇒   R'(4, 3)

and

S(-4, -4)  ⇒   S'(4, 4).

Thus, the required sequence of transformations is

Counterclockwise rotation about the origin by 90 degrees followed by reflection about the x-axis

Option (A) is CORRECT.