Question

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′?

Answer 1

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

Explanation:

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Answer 2

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.


Answer:

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