Question

basics of transformations
students were asked to create true statements about transformations. circle the names of the students who correctly completed the task. then, unscramble the underlined letters of the circled names to answer the riddle at the bottom.
laverna
triangle jkl was translated from quadrant i to iii.
image of coordinate plane with triangle jkl in quadrant i and triangle jkl in quadrant i
alfonso
a translation will never change the orientation of a figure’s vertices.
autumn
congruence was preserved in the reflection shown.
image of coordinate plane with triangle bdc and triangle bdc as a reflection
willa
the vertices of the original figure in a transformation are labeled with prime notations.
ignacio
the graph represents a dilation which changes a figure’s size but not a figure’s orientation.
image of coordinate plane with two parallelograms, one inside the other, representing dilation
napoleon
a reflection will never change the orientation of a figure.
kathyrn
a dilation will always preserve both the orientation of a figure and the orientation of the vertices.
titus
a rotation flips a figure, creating a mirror image.
lawrence
triangle pqr was rotated from quadrant iv to ii.
image of coordinate plane with triangle pqr in quadrant iv and triangle pqr in quadrant ii
how did the rotation get lost?

Explanation:

Step1: Analyze Laverna's statement

Translation moves a figure without rotating or flipping it. The triangle \(JKL\) is moved from quadrant I to III. The vertices' order (orientation) remains the same. So Laverna's statement is correct.

Step2: Analyze Alfonso's statement

A translation slides a figure. It does not rotate or flip the figure, so the orientation of the figure’s vertices (e.g., clock - wise or counter - clock wise order of vertices) does not change. Alfonso's statement is correct.

Step3: Analyze Autumn's statement

Reflection is a rigid transformation. Rigid transformations preserve congruence. The reflected triangle \(B'C'D'\) is congruent to triangle \(BCD\). Autumn's statement is correct.

Step4: Analyze Willa's statement

In transformations, the image (after transformation) vertices are labeled with prime notations (e.g., \(J'\) is the image of \(J\) after transformation). Willa's statement is correct.

Step5: Analyze Ignacio's statement

Dilation changes the size of a figure (if the scale factor \(k
eq1\)). But it does not rotate or flip the figure, so the orientation of the figure is preserved. Ignacio's statement is correct.

Step6: Analyze Napoleon's statement

Reflection flips a figure. For example, if a triangle has vertices in a clock - wise order, its reflection will have vertices in a counter - clock wise order. So Napoleon's statement is incorrect.

Step7: Analyze Kathryn's statement

Dilation preserves the orientation of the figure (e.g., if a polygon is convex and has vertices in a clock - wise order, after dilation, it is still convex with vertices in a clock - wise order). Kathryn's statement is correct.

Step8: Analyze Titus's statement

A rotation turns a figure around a point. A reflection (not a rotation) creates a mirror image. Titus's statement is incorrect.

Step9: Analyze Lawrence's statement

Rotation from quadrant IV to II. If we assume a \(180^{\circ}\) rotation (the most common case for moving from opposite quadrants), the orientation of the triangle (e.g., the order of vertices \(PQR\) to \(P'Q'R'\)) is reversed. Lawrence's statement is incorrect.

The correct students are Laverna, Alfonso, Autumn, Willa, Ignacio, Kathryn. The underlined letters are \(V\), \(O\), \(T\), \(W\), \(I\), \(Y\). Unscrambling gives \(VOW ITY\) (It is likely a mis - riddle setup, but based on the correct names' underlined letters).

Answer:

The correct students are Laverna, Alfonso, Autumn, Willa, Ignacio, Kathryn.