Question

Which sequence of transformations will map figure Q onto figure Q′? Two congruent quadrilaterals are shown on a coordinate plane; quadrilateral Q with coordinates negative 9 comma 2, negative 6 comma 4, negative 4 comma 4, and negative 2 comma 2; quadrilateral Q prime with coordinates 2 comma 2, 4 comma 4, 6 comma 4, and 9 comma 2. Translation of (x, y + 2), reflection over x = 1, and 180° rotation about the origin Translation of (x, y − 2), reflection over x = 1, and 180° rotation about the origin Translation of (x, y − 2), reflection over y = 1, and 180° rotation about the origin Translation of (x, y + 2), reflection over y = 1, and 180° rotation about the origin

Answer 1

The correct transformation sequence to map quadrilateral Q onto Q' includes an 11-unit translation to the right and a reflection over the line x = 1 without any rotation needed.

Step-by-step explanation:

In mathematics, especially geometry, when comparing sequences of transformations that map one figure onto another, one has to consider translations, reflections, rotations, and occasionally dilations. Let's analyze the quadrilaterals Q and Q' given by their coordinates.

The transformation must include shifting quadrilateral Q to the right to make its leftmost x-coordinate equal to that of Q' (from -9 to 2). By counting the units, we see this shift is a translation of 11 units to the right.

After translating, the shapes are congruent but oriented differently. A reflection over the vertical line x = 1 would invert the figure horizontally, which is necessary for Q to match Q'.

Finally, there should be no 180° rotation about the origin since it would send the figure back to the left side of the coordinate plane.

Thus, the sequence of transformations that maps Q onto Q' is a translation of 11 units to the right and a reflection over the vertical line x = 1.