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 down.

Shift the reflected figure 1 unit to the right.

Shift the reflected figure 1 unit up.

Shift the reflected figure 1 unit to the left.

Answer 1

To determine how to correct the reflection over the y-axis, we first need to analyze the original points and their reflected counterparts.

The original points in the first quadrant are:

• A(3, 6)
• B(3, 2)
• C(6, 2)
• D(5, 6)

When reflecting these points over the y-axis, the new coordinates would be:

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

In the second quadrant, the points that are plotted as per your description are:

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

Comparing the reflected points to the plotted points, we see that:

• A'(-3, 6) does not match (-2, 6)
• B'(-3, 2) does not match (-2, 2)
• C'(-6, 2) does not match (-5, 2)
• D'(-5, 6) does not match (-4, 6)

It seems like an error exists. Specifically, the reflected points should be shifted in such a way that their placement aligns with the corresponding points in the second quadrant.

Since on the y-axis the x-coordinates are negative and less than the reflected coordinates, the correct adjustment for each point would involve shifting them to the right (increasing the x-coordinates).

Therefore, the correct response to suggest correcting the reflection is:

Shift the reflected figure 1 unit to the right.