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 down.

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 up.
Shift the reflected figure 1 unit up.
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Answer 1

To determine the correct suggestion for correcting the reflection of the quadrilateral over the y-axis, we need to analyze the original points and their reflections.

The original quadrilateral ABCD has the following coordinates:

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

When reflecting these points over the y-axis, the x-coordinates will change signs:

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

The reflected points should be in the second quadrant, with coordinates:

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

Based on the description of the original second quadrant coordinates provided in the question:

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

We can see that the reflection produced does not match up correctly with the original points in the second quadrant. The reflected quadrilateral is supposed to use the same vertical y-values, but the x-values appear to be incorrect.

To correct the reflection, we notice:

• The x-values should be approximately -3 to align correctly with y-values of 6 and 2.

Since the reflected image should have coordinates aligned at:

• A'(-3, 6)
• B'(-3, 2)

It seems like you actually need to shift the entire reflected figure left to properly align the structure in the second quadrant.

Therefore, the suggestion to correct the reflection should be:

Shift the reflected figure 1 unit to the left.