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 up.
Shift the reflected figure 1 unit up.

Shift the reflected figure 1 unit to the left.

Answer 1

To determine how to correct a reflection over the y-axis, we need to examine how each point of the original figure would be reflected.

Given the coordinates of quadrilateral ABCD:

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

The reflected points in the second quadrant based on the description:

• (−2, 6)
• (−2, 2)
• (−5, 2)
• (−4, 6)

When we compare the reflected points, we see that point C reflects to (-6, 2), but it appears to be plotted at (-5,2) in the second quadrant. Similarly, point D reflects to (-5, 6), but corresponds with (-4,6).

Therefore, it seems that the reflected figure is misaligned by 1 unit to the right, as observed by the coordinates of the points.

To correct this reflection, I would suggest the response:

Shift the reflected figure 1 unit to the left.

This will correctly position the reflected points in their appropriate locations.