Use the image to answer the question.

Question

An illustration shows a coordinate plane. The x-axis and the y-axis range from negative 6 to 6 in one unit increments. Eight points are plotted on the plane. Two quadrilaterals are graphed on the plane. Four points are plotted in the first quadrant. Point A is plotted at the coordinates left parenthesis 3 comma 6 right parenthesis, Point B is plotted at left parenthesis 3 comma 2 right parenthesis, point C is plotted at left parenthesis 6 comma 2 right parenthesis, and point D is plotted at left parenthesis 5 comma 6 right parenthesis. Points A and B, points B and C, points C and D, and points D and A are connected by dotted line segments to form quadrilateral A B C D. Four unlabeled points are plotted in the second quadrant at the coordinates left parenthesis negative 2 comma 6 right parenthesis, left parenthesis negative 2 comma 2 right parenthesis, left parenthesis negative 5 comma 2 right parenthesis, and left parenthesis negative 4 comma 6 right parenthesis. The four points are connected by line segments to form a quadrilateral.

Your friend produced a reflection over the y
-axis that looks like this figure. You notice a problem with the reflection. How would you suggest correcting the reflection?

(1 point)
Responses

Shift the reflected figure 1 unit to the right.
Shift the reflected figure 1 unit to the right.

Shift the reflected figure 1 unit to the left.
Shift the reflected figure 1 unit to the left.

Shift the reflected figure 1 unit down.
Shift the reflected figure 1 unit down.

Shift the reflected figure 1 unit up.
Shift the reflected figure 1 unit up.
Skip to navigation

Answer 1

To determine the correct adjustment for the reflected figure, we first need to understand how the reflection over the y-axis works.

Given the points:

• A(3, 6) reflects to A'(-3, 6)
• B(3, 2) reflects to B'(-3, 2)
• C(6, 2) reflects to C'(-6, 2)
• D(5, 6) reflects to D'(-5, 6)

The reflection would result in points A', B', C', and D' being in the second quadrant.

The description of the problem implies that the reflection generated a figure that does not match the intended result. The coordinates of the original quadrilateral ABCD were in the first quadrant. After reflecting over the y-axis, the expected coordinates of the reflected quadrilateral should be consistent with the second quadrant.

To correct the reflection, we need to consider how the original points were placed and where they would land after the reflection.

If the figure is misplaced in some way after the reflection, it might need a horizontal shift.

In this case, it appears that the entire reflected quadrilateral may need to be moved to align correctly: shifting it 1 unit to the right might be correcting the alignment of those points into their intended positions.

Therefore, the suggested correction is:

Shift the reflected figure 1 unit to the right.