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 (that i described). 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 up.
Shift the reflected figure 1 unit down.
Shift the reflected figure 1 unit to the right.

Answer 1

To analyze the reflection over the y-axis of the quadrilateral formed by the points you described, let's first establish the coordinates after the reflection.

The original coordinates of quadrilateral ABCD are:

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

When these points are reflected over the y-axis, their new coordinates will be:

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

Now, the coordinates of the second quadrilateral in the second quadrant are:

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

When we reflect these points over the y-axis, they become:

• (2, 6)
• (2, 2)
• (5, 2)
• (4, 6)

The reflected quadrilateral from the original quadrilateral ABCD should be in the third quadrant, given that the original points were in the first quadrant. If your friend's reflection is looking incorrect, it's likely that the whole figure shifted improperly or the points did not align with the expected reflection criteria.

To correct the reflection:

1. The reflected points should be translated so that they align with the original reflection quadrilateral.
2. Observing the y-values of the original and how they relate to the grid, the points need to be shifted 1 unit to the right so that the reflected points are now aligned correctly.

Therefore, the correct option would be: Shift the reflected figure 1 unit to the right.