Question

xyz, xyz, xyz, and xyz are shown on the coordinate grid.

1. determine what transformations occurred and in what order:

xyz is first

• translated
• reflected
• rotated
• dilated

to xyz, then

• translated
• reflected
• rotated
• dilated

to xyz,
and finally

• translated
• reflected
• rotated
• dilated

to xyz.

1. describe the transformation for xyz → xyz.

rotated

1. describe the transformation for xyz → xyz.

dilated

1. describe the transformation for xyz → xyz.

rotated

1. write the algebraic description for the sequence of transformations from 7 - 9:

transformation	algebraic description
	(x,y) →
	(x,y) →

Explanation:

Step1: Analyze transformation from XYZ to X'Y'Z'

If a rotation about the origin occurs, for a 90 - degree counter - clockwise rotation, the algebraic rule is $(x,y)\to(-y,x)$. Let's assume the rotation is 90 - degree counter - clockwise about the origin.

Step2: Analyze transformation from X'Y'Z' to X''Y''Z''

For a dilation centered at the origin with a scale factor $k$, the algebraic rule is $(x,y)\to(kx,ky)$.

Step3: Analyze transformation from X''Y''Z'' to X'''Y'''Z'''

Assuming a 90 - degree counter - clockwise rotation about the origin again, the rule is $(x,y)\to(-y,x)$.

Answer:

Transformation	Algebraic Description
Dilation (centered at origin with scale factor $k$)	$(x,y)\to(kx,ky)$
Rotation (90 - degree counter - clockwise about origin)	$(x,y)\to(-y,x)$