What are the coordinates of A’ after the reflection across the line x= 3

add an image

step-by-step explanation:

step-by-step explanation:

rectangles are made up of 4 right angles, which means that a side and a base meet perpendicular to one another.   their slopes then have to reflect perpendicular slopes.   perpendicular slopes are opposite reciprocals of one another.   for example, if the slope of one line is +2/3, then the perpendicular slope to that would be -3/2.   so we look for that combination in our choices.

all of them satisfy that condition (so what's the question, i guess? )

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81