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.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

answer: no, but if it does it's a obvious pattern.

step-by-step explanation: