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.

Question

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

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

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.

Answer 1

To determine how to correct the reflection over the y-axis, let's first consider how the coordinates of the original points would change with a reflection.

The original quadrilateral \( ABCD \) has the points:

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

When reflecting a point \((x, y)\) over the y-axis, the new coordinates will be \((-x, y)\). Therefore, the reflected points will be:

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

Now, looking at the original points in the second quadrant:

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

After reflection, the quadrilateral constructed from these points should match the respective reflected coordinates. However, after performing the reflection, it should be clear that points A' through D' do not perfectly align with the second quadrant's reflected form as per your friend’s illustration.

The discrepancy arises from the specific coordinates plotted in the second quadrant. It’s likely that the reflection isn't correctly aligned.

Since the reflection of the original points produces new coordinates that are not matched by the points in the second quadrant, one possible correction might involve shifting.

Looking closely at the x-coordinates before and after the reflection can help determine how to shift the points:

• Point B's reflected coordinate should be at \( (-3, 2) \), but it aligns with a point already on the second quadrant.
• The same goes for points D and C.

If they're off by one unit, we can ascertain that the coordinates need to be shifted.

Based on this analysis, if the reflected positions are all incorrectly placed within the second quadrant relative to their x-values and need to correct by adding units directed towards the y-value alignment, you would shift the reflected figure 1 unit to the left.

So, the answer is: Shift the reflected figure 1 unit to the left.