Polygons efhg and e′f′h′g′ are shown on the following coordinate grid: a coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. a polygon efhg is shown with vertex e on ordered pair 2, 2, vertex f on ordered pair 2, 4, vertex h on ordered pair 3, 5 and vertex g on ordered pair 3, 1. a polygon e prime f prime h prime g prime is shown with vertex e prime on ordered pair negative 1, 2, vertex f prime on ordered pair negative 3, 2, vertex h prime on ordered pair negative 4, 3, and vertex g prime on ordered pair 0, 3. what set of transformations is performed on efhg to form e′f′h′g′?

Check the first picture. Our goal is to map  EFHG to  E′F′H′G′.

All choices involve a rotation by 90° or 270° counterclockwise about the origin.

consider a rotation by 90° counterclockwise. Each point P(a, b) can be rotated 90° cwise about the origin to form P"(a",b") :

by drawing the right angle POP", such that |PO|=|OP"|.

or by plotting each P"(a",b") so that  (a",b")=(-b, a)

for example if G(3, 1) is mapped to G(-1, 3) by either of the procedures described.

check picture 2.

EFHG  is mapped to E′'F'′H'′G′'.

In order to map E′'F'′H'′G′' to E'F′H'G′, we need to translate the figure 1 unit right.

 

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