If quadrilateral resp is is reflected across the line y = 2x +7 and again across the line y = -12x + 5, what will be the resulting image? a. the resulting image will be a translation of the pre-image b. the resulting image will be a rotation of the pre-image c. the resulting image will be a reflection of the pre-image d. the resulting image cannot be determined

The first reflection reverses the orientation and alters the direction of the vectors representing the sides of the quadrilateral. The second reflection does the same thing. The end result is that the orientation is unchanged by two reflections, and the direction of the sides of the quadrilateral is changed.

The appropriate choice is ...

... B. The resulting image will be a rotation of the pre-image.

_____

The center of rotation will be the point where the lines cross. (That is the invariant point.)

In the attachment, the green quadrilateral RESP is reflected across the line y=2x+7 (blue) to form the blue quadrilateral R'E'S'P'. That is then reflected across the line y = -12x +5 (orange) to give the orange quadrilateral R"E"S"P", which is a rotation of the pre-image.

The amount of rotation is double the angle between the lines, about 62.7°.

answer with step-by-step explanation:

a. ∠j is supplementary to ∠k - true:

(opposite angles of a trapezoid are supplementary which means that they add up to 180 degrees)

b. kl is parallel to jm - true:

(opposite sides are parallel to each other in a trapezoid)

c. jk is perpendicular to kl - false:

(clearly, jk does not make a right angle with kl)

d. jk is parallel to lm - false:

(jk and lm are two lines opposite in direction to each other so they cannot be parallel)

e. ∠j is congruent to ∠m - true:

(the angles on each side of the base are congruent)

f. ∠j is congruent to ∠k - false:

(the angles on the same side but opposite side of the base are not congruent)

ik how do do this just give me a few minutes and i will give it to