Question

unit 4 lesson 3 homework
triangles rzk, rzk, and rzk are shown on the coordinate grid where △rzk is the preimage.

1. describe the feature of △rzk that indicates the rigid motion that was applied to △rzk that resulted in △rzk.
2. show the feature described by mapping the transformation of one vertex of △rzk to △rzk.
3. complete the table.

transformation	mapping	algebraic description

1. map the transformation of one vertex of △rzk to △rzk.
2. complete the table.

transformation	mapping	algebraic description

Explanation:

Step1: Observe the transformation from △RZK to △R'Z'K'

The shape and size are the same, indicating a translation.

Step2: Map a vertex

Let's take vertex R. If R has coordinates (x,y), and R' has coordinates (x + a,y + b), we find the change in x - and y - values. Suppose R(-4,1) and R'( - 1,1), the translation is 3 units to the right (x - value changes by 3) and 0 units in the y - direction.

Step3: Complete the first table

The transformation is a translation. The mapping is △RZK→△R'Z'K'. The algebraic description for a point (x,y) in △RZK to a point (x',y') in △R'Z'K' is (x,y)→(x + 3,y).

Step4: Observe the transformation from △R'Z'K' to △R''Z''K''

It appears to be a rotation. Let's take vertex R'. If R'(-1,1) and R''(0,-2), we analyze the rotation rules.

Step5: Complete the second table

The transformation is a rotation. The mapping is △R'Z'K'→△R''Z''K''. For a 90 - degree clockwise rotation about the origin, the algebraic description for a point (x,y) in △R'Z'K' to a point (x',y') in △R''Z''K'' is (x,y)→(y,-x).

Answer:

1. The shape and size of △R'Z'K' are the same as △RZK, indicating a translation.
2. For example, if R has coordinates (-4,1) and R' has coordinates (-1,1), the x - value of R increases by 3 and the y - value remains the same.
3. Transformation: Translation; Mapping: △RZK→△R'Z'K'; Algebraic Description: (x,y)→(x + 3,y)
4. For example, if R' has coordinates (-1,1) and R'' has coordinates (0,-2), it shows a 90 - degree clockwise rotation about the origin.
5. Transformation: Rotation; Mapping: △R'Z'K'→△R''Z''K''; Algebraic Description: (x,y)→(y,-x)