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Use the image to answer the 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 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.

1 answer

To correct the reflection of the quadrilateral over the y-axis, we need to analyze the coordinates of the original quadrilateral A B C D and how they transform when reflected.

The points for quadrilateral A B C D are:

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

When we reflect these points over the y-axis, the new coordinates would be:

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

The original quadrilateral is located in the first quadrant, while the coordinates after the reflection would be located in the second quadrant.

The reflected points would not align with the points in the second quadrant given in the description. The points in the second quadrant are:

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

To further analyze:

  • A' (-3, 6) should correspond to (-2, 6).
  • B' (-3, 2) should correspond to (-2, 2).
  • C' (-6, 2) would correspond to (-5, 2).
  • D' (-5, 6) would correspond to (-4, 6).

To match the reflected figure with the given coordinates, we notice that you'd need to shift the figure up or down vertically to align the y-coordinates.

Upon checking:

  • The y-coordinates of (-3, 6) and (-3, 2) for A' and B' could be shifted up to align with (-2, 6) and (-2, 2).

Thus, the best suggestion would be:

Shift the reflected figure 1 unit up.