Question

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lesson 4.4 practice exercise #5
use the item bank below.
determine whether the polygons with the given vertices are congruent. use transformations to explain your reasoning.
q(2,4), r(5,4), s(4,1) and t(6,4), u(9,4), v(8,1)
________, △tuv is ________ of △qrs.
item bank:
no yes a 180° rotation a reflection in the x - axis a translation 4 units right a translation 5 units up not a rigid motion

1. medium

lesson 4.4 practice exercise #7
use the item bank below.
determine whether the polygons with the given vertices are congruent. use transformations to explain your reasoning.
j(1,1), k(3,2), l(4,1) and m(6,1), n(5,2), p(2,1)
________, △jkl is ________ of △mnp.
item bank:
no yes a 90° counterclockwise rotation a reflection in the y - axis a translation 4 units left a translation 5 units down not a rigid motion

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lesson 4.4 practice exercise #22
error analysis: identify and correct the error in describing the congruence transformation.
rectangle abcd is mapped to rectangle abcd by a translation 3 units down and a reflection in the y - axis.

Explanation:

5.

Step1: Check x - coordinates change

For point Q(2,4) and T(6,4), the x - coordinate of T is 4 units more than that of Q. For R(5,4) and U(9,4), 9 - 5=4. For S(4,1) and V(8,1), 8 - 4 = 4.

Step2: Check y - coordinates

The y - coordinates of corresponding points are the same. So, ΔTUV is a translation 4 units right of ΔQRS. Since translation is a rigid - motion and rigid - motions preserve congruence, the polygons are congruent.

Step1: Analyze the transformation

If we consider the transformation of points from △JKL to △MNP. Let's check the x - coordinates. For J(1,1) and M(6,1), the change in x is 5. For K(3,2) and N(5,2), the change in x is 2. For L(4,1) and P(2,1), the change in x is - 2. There is no single rigid - motion transformation (rotation, reflection, or translation) that can map △JKL to △MNP.

Step1: Identify the correct transformation

If we first translate rectangle ABCD 3 units down, and then reflect it in the y - axis, the order of transformations matters. The error is in the order of description. First, reflecting rectangle ABCD in the y - axis and then translating 3 units down will give the correct mapping. When we reflect in the y - axis, the x - coordinates of the points change their signs. Then, when we translate 3 units down, the y - coordinates of the points are decreased by 3.

Answer:

yes, a translation 4 units right

6.