Congruence and Transformations Answers

A teacher asks students to determine the accuracy of this statement.A reflection over the x-axis and then over the y-axis results in the same transformation as a 180 rotation about the origin of the original figure.Kwame’s explanation of the accuracy of the statement is shown below.Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3). Step 2: Reflect the pre-image over the x-axis: (1, –2), (1, –4), (2, –3).Step 3: Reflect the figure from step 2 over the y-axis: (–1, 2), (–1, 4), (–2, 3).Step 4: Rotate the pre-image 180: (–1, –2), (–1, –4), (–2, –3).Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate.Which best explains Kwame’s solution?

Harley graphs a polygon that is located entirely inside quadrant I. He rotates the figure clockwise 90 about the origin and then reflects the rotated figure over the x-axis. He translates the resulting figure 3 units to the left and 3 units up. Which best describes the location of the final image?

Triangle ABC is rotated 180º using the origin as the center of rotation.Which sequence of transformations will produce the same result?

Triangle ABC is shown with four images that are each the result of a transformation of triangle ABC.For which triangle is one reflection necessary for the transformation to occur?

The vertices A(–2, –1), B(–3, 2), C(–1, 3), and D(0, 0) form a parallelogram. The vertices A’(–1, –2), B’(2, –3), C’(3, –1), and D’(0, 0) are the image of the parallelogram after a sequence of transformations. Which sequence of transformations could produce the image from the pre-image?

Square ABCD is shown with four congruent images such that ABCD FGHI JKLM NOPQ RSTU. For which square is a reflection necessary to produce the transformed figure?

Figure X is translated down 5 and then reflected over the y-axis, forming figure Y. Which sequence of transformations results in the same transformation?

Triangle MNO is reflected over the x-axis and then translated up 4 and right 3. How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?

Triangle MNO is rotated 180 using the origin as the center of rotation. Which sequences of transformations will produce the same results? Check all that apply.

Chareese reflects figure RSUT over the y-axis and then rotates the reflected figure 180 about the origin, resulting in figure A. She states that . Which best describes the accuracy of her congruency statement?