Reflections Across the x- or y- Axis Quick Check

Question

2 of 52 of 5 Items
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 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.

Answer 1

To determine how to correct the reflection of the quadrilateral over the y-axis, we first need to analyze the original points and their corresponding reflections.

The original points in quadrilateral ABCD are as follows:

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

When reflecting over the y-axis, the rule is to change the sign of the x-coordinate while keeping the y-coordinate the same. Thus, the reflections of these points would be:

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

Now, let's look at the coordinates of the points you mentioned for the second quadrilateral which were plotted in the second quadrant:

• Point 1: (-2, 6)
• Point 2: (-2, 2)
• Point 3: (-5, 2)
• Point 4: (-4, 6)

After comparing the reflectively calculated coordinates with the provided coordinates, it seems that the reflection is not correct based on the expected placement of reflected points.

Since all the reflected points should be to the left in a matching manner but here the points from the reflection end up at different locations, you would need to shift the reflected figure:

Given that the original points from quadrilateral ABCD should map to their reflected points in the second quadrants coordinates as follows, it seems the reflected figure is not correctly positioned on the coordinate plane. To correct this, you would need to shift the figure accordingly, considering how far it is from where it needs to be.

Based on the choices provided, since the coordinates of the reflected quadrilateral must end up being in more negative x-coordinates, the correct move would be to shift the reflected figure 1 unit to the left.

Thus the response would be: Shift the reflected figure 1 unit to the left.