Question

Question

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

Shift the reflected figure 1 unit up.
Shift the reflected figure 1 unit up.

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 the necessary correction for the reflection over the y-axis, we should evaluate the coordinates of the points in the original quadrilateral (ABCD) and their reflected counterparts.

1. Original Points:

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

   When reflected over the y-axis, the x-coordinates change signs:

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

2. Reflected Points: The reflection should produce these new coordinates in the third quadrant:

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

   However, the problem mentions that the reflected points were plotted incorrectly in the second quadrant:

   • The reflected coordinates were incorrectly noted as (-2, 6), (-2, 2), (-5, 2), and (-4, 6).

3. Analyzing the Shift:

   • The correctly reflected points in the second quadrant are not matching the expected coordinates from the original reflection requirements.
   • It looks like the reflected points need to be adjusted horizontally. Observing that an x-coordinate (-3) doesn't match the given (-2) indicates that the reflected figure needs to be shifted.

To fix the reflection, correcting the x-coordinates is needed. Specifically, the reflected figure needs to be shifted 1 unit to the left to align it correctly with their intended reflections.

Correct answer: Shift the reflected figure 1 unit to the left.