Question

1. medium 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) yes, △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 6. 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 7. medium lesson 4.4 practice exercise #22 error analysis: identify and correct the error in descbingthe congruence transformation. x rectangle abcd is mapped to rectangle abcd by a translation 3 units down and a reflection in the y - axis.

Explanation:

5.

Step1: Analyze x - coordinates

For point \(Q(2,4)\) and \(T(6,4)\), \(6 - 2=4\); for \(R(5,4)\) and \(U(9,4)\), \(9 - 5 = 4\); for \(S(4,1)\) and \(V(8,1)\), \(8 - 4=4\). The y - coordinates remain the same.

Step2: Determine transformation

The transformation from \(\triangle QRS\) to \(\triangle TUV\) is a translation 4 units right. Since translation is a rigid - motion and rigid - motions preserve congruence, the two triangles are congruent.

Step1: Analyze x - coordinates

For point \(J(1,1)\) and \(M(6,1)\), \(6 - 1 = 5\); for \(K(3,2)\) and \(N(5,2)\), \(5 - 3=2\); for \(L(4,1)\) and \(P(2,1)\), \(2 - 4=-2\).
We can observe that if we consider the transformation of \(\triangle JKL\) to \(\triangle MNP\), we note that the x - coordinates of the vertices of \(\triangle JKL\) and \(\triangle MNP\) do not follow a simple translation or rotation rule.
If we consider a reflection, we can see that \(\triangle JKL\) and \(\triangle MNP\) are not reflections of each other.
Since there is no rigid - motion (translation, rotation, reflection) that maps \(\triangle JKL\) onto \(\triangle MNP\), they are not congruent.

Step1: Identify the error

The error is in the order of transformations. If we first translate rectangle \(ABCD\) 3 units down and then reflect it in the \(y\) - axis, the orientation of the rectangle will be incorrect.
The correct order should be first reflect in the \(y\) - axis and then translate 3 units down.

Step2: Correct the transformation

Rectangle \(ABCD\) is mapped to rectangle \(A'B'C'D'\) by a reflection in the \(y\) - axis and then a translation 3 units down.

Answer:

yes, a translation 4 units right

6.