Transformations

On the set of axes below, congruent parallelograms ABCD and RSTU are graphed. Which sequence of transformations maps ABCD onto RSTU?

• a reflection over the x-axis followed by a translation ten units to the left and one unit up

• a translation four units down followed by a reflection over the y-axis

• a reflection over the y-axis followed by a translation of two units down

• a translation ten units to the left followed by a reflection over the x-axis

In parallelogram ABCD below, diagonals AC and BD intersect at E. Which transformation would map △ABC onto △CDA?

• a reflection over AC

• a reflection over DB

• a clockwise rotation of 90° about point E

• a clockwise rotation of 180° about point E

In the diagram below, quadrilateral BCDE maps onto quadrilateral JKLM using a sequence of rigid motions. Determine and state the degree measure of angle D.

• 45 degrees

• 60 degrees

• 90 degrees

• 120 degrees

Trapezoid ABCD is graphed on the set of axes below. Which transformation would map point A onto A'?

• reflection over y = x

• reflection over the y-axis

• rotation of 180° about (0,0)

• rotation of 90° counterclockwise about (0,0)

A rectangle is graphed on the set of axes below. A reflection over which line would carry the rectangle onto itself?

• y = 2

• y = 10

• 6

• 16

• 20

• 28

Triangles YEG and POM are two distinct non-right triangles such that angle G is congruent to angle M. Which statement is sufficient to prove triangle YEG is always congruent to triangle POM?

• C. There is a sequence of rigid motions that maps \overline{LE} onto \overline{LO} and \overline{YE} onto \overline{PO}.

• D. There is a sequence of rigid motions that maps point Y onto point P and \overline{YG} onto \overline{PM}.

• a rotation

• a line reflection

• a translation followed by a dilation

• a line reflection followed by a second line reflection

Trapezoid is drawn such that the top and bottom sides are parallel. A second trapezoid is the image of the first after a rotation. Which statement is always true?