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.

Question

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?

translate by (__)

Answer 1

To determine that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I, the next step after rotating the first rectangle 90 degrees clockwise about the origin is to translate by (2, 6).

After the rotation, the coordinates of the first rectangle will transform, and then you will need to move it to match the position of the second rectangle (Quadrant I). The translation by (2, 6) moves the rectangle to the correct location.