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

Shift the reflected figure 1 unit down.
Shift the reflected figure 1 unit down.

Shift the reflected figure 1 unit to the right.

Answer 1

To determine how to correct the reflection of quadrilateral ABCD across the y-axis, we first need to analyze the coordinates of the points before and after the reflection.

The original coordinates of quadrilateral ABCD are:

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

After reflecting over the y-axis, the coordinates should be:

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

Now we look at the points in the second quadrant:

• The coordinates of points are:
  • P1(-2, 6)
  • P2(-2, 2)
  • P3(-5, 2)
  • P4(-4, 6)

Comparing the reflected positions with the original positions, we can see that the reflected points do not match the expected coordinates. Hence, to correct the reflection, we can note that points P1 and P2 are each 1 unit to the right of their reflected positions.

Thus, the correct response to suggest is: Shift the reflected figure 1 unit to the left.