Question

Use the image to answer the question.

A coordinate plane with 4 quadrants shows x and y axes ranging from negative 8 to 8 in increments of 1. Two rectangles are formed by lines joining four plotted points each. The coordinates of the plotted points for first rectangle joined by solid lines are left parenthesis negative 1 comma negative 2 right parenthesis, left parenthesis negative 3 comma negative 2 right parenthesis, left parenthesis negative 3 comma negative 7 right parenthesis, and left parenthesis negative 1 comma negative 7 right parenthesis. The coordinates for the second rectangle joined by lines made of dashes and dots are left parenthesis 2 comma 3 right parenthesis, left parenthesis 7 comma 3 right parenthesis, left parenthesis 7 comma 5 right parenthesis, and left parenthesis 2 comma 5 right parenthesis.

To show that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I, Darnell rotates the first rectangle 90 degrees clockwise into Quadrant II. What is his next step?

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Remaining Attempts : 3

Answer 1

To successfully rotate the first rectangle 90 degrees clockwise into Quadrant II and make it congruent to the rectangle in Quadrant I, Darnell needs to move the rotated rectangle to the corresponding position in Quadrant II, which involves translating its coordinates.

The original coordinates of the rectangle in Quadrant III are:
- (-1, -2)
- (-3, -2)
- (-3, -7)
- (-1, -7)

After rotating 90 degrees clockwise, the new coordinates will be:
- (-2, 1) (originally (-1, -2))
- (-2, 3) (originally (-3, -2))
- (-7, 3) (originally (-3, -7))
- (-7, 1) (originally (-1, -7))

Now, to position this rectangle in Quadrant II, Darnell's next step will be to translate the rectangle to match the position of the rectangle in Quadrant I.

To specify the final location of the rectangle and confirm its coordinates, we evaluate the translation:
- The x-coordinates will need to be adjusted to negative values (moving left) and y-coordinates to positive (moving up).

The dashed rectangle in Quadrant I has coordinates:
- (2, 3)
- (7, 3)
- (7, 5)
- (2, 5)

Since the second rectangle is already defined by these coordinates, to recreate the first rectangle to a congruent position, Darnell needs to ensure it fits the congruent properties regarding the rectangle's position and dimensions.

The last step after rotation will generally involve translating the rectangle based on the established congruence. The coordinates for this complete transformation after Darnell’s movement should be identified.

You need to specify the final coordinates to determine Darnell's exact steps in terms of translation or if there are specific coordinates to move. If we need to mention the specific translation, we may conclude it could be from Quadrant II to coordinates where they would mirror in position, such as moving back to the same height or width in dimension layout across both quadrants.

Thus the completion could possibly say the translation is needed of:
**Translate to ensure coordinates mirror across QI & QIII]**, using points such as:
(-7, 3), (-7, 5), (-2, 3), (-2, 5) in respect to either the specified congruence or defined rectangle setup based on which quadrants were properly structured.

A clearer answer would involve coordinates indicating:
**Final Position: (x,y) to x being <-2 or -7 based on previous completion steps for congruency alignment.**