Figure EFGH is transformed to E′F′G′H′, as shown: A coordinate plane is shown. Figure EFGH has vertices E at negative 5 comma 4, F at negative 5 comma 1, G at negative 3 comma 2, and H at negative 1 comma 6. Figure E prime F prime G prime H prime has vertices at E prime 7 comma 4, F prime 7 comma 1, G prime 5 comma 2 and H prime 3 comma 6.
Which of the following sequences of transformations is used to obtain figure E′F′G′H′ from EFGH? (4 points)

Question 4 options:

1)

Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units

2)

Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units

3)

Reflection about the y-axis followed by a translation right by 2 units

4)

Reflection about the x-axis followed by a translation left by 2 units

It is helpful to plot the points, then mentally test the answers for plausibility. Translation of E 1 unit to the right puts it at (2, 1), then rotation counterclockwise 90° about the origin puts it at (-1, 2), the location of E'.

The appropriate choice seems to be

 A translation 1 unit to the right followed by a 90-degree counterclockwise rotation about the origin

_____

Translation 1 unit right: (x, y) ⇒ (x+1, y)

Rotation 90° CCW: (x, y) ⇒ (-y, x)

Both transformations in that order: (x, y) ⇒ (-y, x+1)

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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