Question

Brainliest and 11 pts!

Answer 1

Answer:

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

Step-by-step explanation:

Given

E(1,1)

F(1,4)

G(5,4)

H(4,1)

A translation 1 unit to the right transform point (x, y) to (x+1, y)

A 90-degree counterclockwise rotation about the origin transform point (x,y) to (-y,x). Then, (x+1, y) is transformed into (-y,x+1). Applying this to Polygon EFGH  we get

E(1,1)  -> E'(-1,2)

F(1,4)  -> F'(-4,2)

G(5,4)  -> G'(-4,6)

H(4,1) -> H'(-1,5)

Answer 2

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)