Question

do you know how? in 4 - 6, use the diagram below. 4. describe a sequence of transformations that maps rectangle wxyz onto rectangle wxyz. 5. describe another way that you could map rectangle wxyz onto wxyz. 6. draw the image of rectangle wxyz after a reflection across the line y = 1 and a translation 1 unit right. label the image wxyz.

Explanation:

Step1: Analyze the position change

First, observe the relative positions of the two rectangles in the coordinate - plane. We can use translation and reflection to map one rectangle onto the other.

Step2: First sequence of transformations for question 4

A possible sequence is a reflection across the y - axis followed by a translation. Reflect rectangle WXYZ across the y - axis. If a point (x,y) in rectangle WXYZ is reflected across the y - axis, its new coordinates become (-x,y). Then, translate the reflected rectangle up by a certain number of units (by observing the vertical distance between the two rectangles).

Step3: Another sequence for question 5

We could first translate rectangle WXYZ up to the same horizontal level as rectangle W'X'Y'Z', and then reflect it across the y - axis.

Step4: For question 6

To reflect a point (x,y) across the line y = 1, the formula for the reflection is (x,2 - y). After reflecting each vertex of rectangle WXYZ across the line y = 1, then translate each of the reflected points 1 unit to the right. For a point (x,y) after reflection across y = 1 getting (x,2 - y), after translation 1 unit right, the new point is (x + 1,2 - y). Then label the new rectangle as W''X''Y''Z''.

Answer:

1. Reflect across the y - axis and then translate up.
2. Translate up first and then reflect across the y - axis.
3. Follow the steps of reflection across y = 1 (using the rule (x,2 - y)) and then translation 1 unit right (using the rule (x+1,2 - y)) to draw and label the new rectangle W''X''Y''Z''.