Ben performed a transformation on trapezoid pqrs to create p‘ q‘ r‘ s‘, as shown in the figure below what transformation did ben perform to create p‘ q‘ r‘ s‘ ?

The answer is D: rotation of 90° counterclockwise about the origin

Step-by-step explanation:

 The correct option is

(D) Rotation of 90° counterclockwise about the origin.

Step-by-step explanation:  Given that Ben performed a transformation on trapezoid PQRS to create P'Q'R'S' as shown in the figure.

We are to find the transformation that Ben performed to create P'Q'R'S'.

From the graph, we note that

the co-ordinates of the vertices of trapezoid PQRS are P(-6, -3), Q(-4, -3), R(-2, -5) and S(-7, -6)

and the co-ordinates of the vertices of trapezoid P'Q'R'S' are P'(3, -6), Q'(3, -4), R'(5, -2) and S'(6, -7).

So, the transformations of the vertices of PQRS to the vertices of P'Q'R'S' are

P(-6, -3)  ⇒  P'(3, -6)

Q(-4, -3)  ⇒  Q'(3, -4)

R(-2, -5)  ⇒  R'(5, -2)

S(-7, -6)  ⇒  S'(6, -7)

Therefore, if (x, y) is a vertex of trapezoid PQRS, then the corresponding vertex of P'Q'R'S' is (-y, x).

That is, (x, y)  ⇒  (-y, x).

This gives the rotation of (x, y) by 90° counterclockwise about the origin.

Thus, option (D) is CORRECT.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.