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'?
rotation of 270° counterclockwise about the origin
reflection across the line of symmetry of the figure
reflection across the y-axis
rotation of 90° counterclockwise about the origin

answer:   the correct option is

(d) rotation of 90° counterclockwise about the origin.

step-by-step explanation:   given thatben performed a transformation on trapezoid pqrs to create p'q'r's' as shown in the figure.

we are to select the correct transformation that ben performed to create p'q'r's'.

the co-ordinates of the vertices of trapezoid pqrs are

p(-6, -3), q(-4, -3), r(-2, -5) and s(-7, -6).

and, 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,

p(-6, -3)   ⇒   p'(3, -6),

q(-4, -3)   ⇒ q'(3, -4),

r(-2, -5)   ⇒   r'(5, -2),

s(-7, -6)   ⇒   s'(-6, 7).

so, the transformation rule from trapezoid pqrs to p'q'r's' is

(x, y)   ⇒   (-y, x), which gives rotation about the origin (0, 0) through an angle of 90° counterclockwise or 270° clockwise.

since 270° clockwise rotation about the origin is not in the given options, so   the required transformation is

"rotation of 90° counterclockwise about the origin."

thus, (d) is the correct option.

step-by-step explan mxfcg'k; uafwgzfgjhklhgation:

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.