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.

Question

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? translate ()

Answer 1

After rotating the first rectangle (in Quadrant III) 90 degrees clockwise into Quadrant II, Darnell's next step would be to translate the newly positioned rectangle in Quadrant II so that it matches the position of the second rectangle in Quadrant I.

To do this, Darnell would need to determine the translation vector that moves the rectangle from its new location in Quadrant II to the corresponding location in Quadrant I. The translation would involve moving the rectangle right and up to align it with the coordinates of the second rectangle in Quadrant I.

This would result in the two rectangles being congruent to each other as the dimensions would remain the same.