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 up.
Shift the reflected figure 1 unit up.

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.
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Answer 1

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

Given the original points in the first quadrant:

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

When reflected over the y-axis, the coordinates of the points would change as follows:

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

Now, let's analyze the coordinates of the points in the second quadrant that are mentioned:

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

For the reflection to be correct, the reflected points should match these coordinates.

Comparing the reflected points with these coordinates, we see:

• A'(−3, 6) does not match with any point.
• B'(−3, 2) does not match with any point.
• C'(−6, 2) matches with (−5, 2) which indicates a potential shift.
• D'(−5, 6) matches with (−4, 6) which indicates a similar potential shift.

The pattern shows an inconsistency, indicating that the entire reflected figure needs to be shifted to match the points in the second quadrant.

To solve for the specific shifts:

• All of the reflected points need to be shifted right by 1 unit (i.e., from (−3, 6) to (−2, 6), etc.) to align with the quadrilateral formed in the second quadrant.

Thus, the correct suggestion to adjust the reflection over the y-axis is to:

Shift the reflected figure 1 unit to the right.