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)

9

step-by-step explanation: