Congruence and Transformations

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

Accurate. A reflection will change the direction the vertices trace around the figure. A rotation preserves the change.

Jason states that triangle ABC is congruent to RST . Kelley states that triangle ABC is congruent to TSR . Which best describes the accuracy of the congruency statements?

Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.

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?

GHI

Which sequence of transformations produces A'B'C' from ABC?

a translation up 3 and then a 90º counterclockwise rotation about the origin

Triangle ABC is rotated 180º using the origin as the center of rotation. Which sequence of transformations will produce the same result? a translation up 4 and then a reflection over the y-axis a translation up 4 and then a translation right 6 a reflection over the x-axis and then a reflection over the y-axis a translation right 6 and then a reflection over the x-axis

a reflection over the x-axis and then a reflection over the y-axis

Harley graphs a polygon that is located entirely inside quadrant I. He rotates the figure clockwise 90 degree 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? quadrant I quadrant II above the x-axis left of the y-axis

above the x-axis

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 180mc021-1.jpg 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 180mc021-2.jpg: (-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?

Kwame's explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.

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?

RSTU

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?

a reflection over the y-axis and then a 90 degree clockwise rotation about the origin

Figure G is rotated 90 degree clockwise about the origin and then reflected over the x-axis, forming figure H. Which sequence of transformations will produce the same results? a reflection over the y-axis and then a rotation 90 degree clockwise about the origin a reflection over the x-axis and then a rotation 90 degree clockwise about the origin a 180 degree rotation about the origin a reflection over the y-axis and then a reflection over the x-axis

a reflection over the y-axis and then a rotation 90 degree clockwise about the origin

Ethan created three triangles: triangle X, triangle Y, and triangle Z. If triangle Y is congruent to X and triangle Y is congruent to Z, which must also be true? The triangles are equilateral. The triangles are right triangles. Triangles X and Z are congruent. Triangles X, Y, and Z share one or more vertices.

Triangles X and Z are congruent

Alexi transformed figure L such that its image is figure K after a 90 degree counterclockwise rotation about the origin and a reflection over the y-axis. Jonathan used figure L to perform the same transformation, but he reflected figure L over the y-axis before performing the 90 degree counterclockwise rotation. Which best compares Alexi's and Jonathan's transformed figures? The change in order will not affect the final image. Their transformed figures will be identical. The change in order will result in the transformed images having vertices in the same location, but in a different orientation. The change in order will result in the transformed image of figure L being transformed back onto figure L. The change in order will result in the transformed image of figure L having a different location.

The change in order will result in the transformed image of figure L having a different location.

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?

Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.

Triangle RST is translated 2 units left and then reflected over the y-axis. Which transformations of RST will result in the same image? Check all that apply

a reflection over the y-axis and then a translation 2 units right a 180 degree rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis