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A coordinate plane with 4 quadrants shows x and y axes ranging from negative 9 to 9 in increments of 1. Three 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 5 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 4 right parenthesis, left parenthesis negative 1 comma negative 6 right parenthesis, and left parenthesis negative 5 comma negative 6 right parenthesis. The coordinates for the second rectangle joined by lines made of dashes and dots are left parenthesis 3 comma 4 right parenthesis, left parenthesis 5 comma 4 right parenthesis, left parenthesis 5 comma 8 right parenthesis, and left parenthesis 3 comma 8 right parenthesis. The coordinates of the plotted points for the third rectangle joined by dotted lines are left parenthesis negative 4 comma 1 right parenthesis, left parenthesis negative 6 comma 1 right parenthesis, left parenthesis negative 6 comma 5 right parenthesis, and left parenthesis negative 4 comma 5 right parenthesis.
The first step to determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I was to rotate the first rectangle 90 degrees clockwise about the origin. What is the next step?

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2 answers

After rotating the first rectangle (in Quadrant III) 90 degrees clockwise about the origin, the next step is to check if the dimensions of the rectangle match those of the rectangle in Quadrant I.

To do this, you should calculate the widths and heights of both rectangles and confirm that they are equal.

Thus, if the dimensions (width and height) of the rotated rectangle correspond to those of the rectangle in Quadrant I, then you can conclude that the two rectangles are congruent.

So, summarizing the steps:

  1. Rotate the rectangle in Quadrant III 90 degrees clockwise about the origin.
  2. Compare the dimensions to determine congruence.

If you want the specific dimensions or coordinates after rotation, please indicate!

Yes I want specific coordinates please