What set of transformations are applied to parallelogram abcd to create a″b″c″d″?
'parallelogram formed by ordered pairs a at negative 4, 1, b at negative 3, 2, c at negative 1, 2, d at negative 2, 1. second parallelogram transformed formed by ordered pairs a double prime at 1, negative 4, b double prime at 2, negative 3, c double prime at 2, negative 1, d double prime 1, negative 2.

(1) it's a counterclockwise 90° and then reflection over Y axis transformation

(2) or just reflection across y = x

Step-by-step explanation:

A   (-4 , 1)     B  (-3 , 2)    C  (-1 , 2)    D  (-2, 1)

A'' (1 , -4)     B'' (2 , -3)    C'' (2 , -1)   D'' (1, -2)

First step: 90 degree rotation counterclockwise around the origin

(x, y) ->  (-y, x)

A'  (-1 , -4)     B' (-2 , -3)    C' (-2 , -1)    D' (-1, -2)

2nd step: reflection across Y axis, negate the value of the x-coordinate of each point, but leave the y value the same

(x, y) -> (-x, y)

A'' (1 , -4)     B'' (2 , -3)    C'' (2 , -1)   D'' (1, -2)

2nd resolution: Reflection across y = x

(x, y) -> (y, x)

A   (-4 , 1)     B  (-3 , 2)    C  (-1 , 2)    D  (-2, 1)

A'' (1 , -4)     B'' (2 , -3)    C'' (2 , -1)   D'' (1, -2)

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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