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?

(1 point)
translate by ().

Answer 1

To translate the rectangle from Quadrant III to Quadrant I after rotating it 90 degrees clockwise about the origin, you need to move it horizontally and vertically into the positive x and y coordinates.

Assuming the rectangle in Quadrant III is located with its vertices at points with negative x and y coordinates (for instance, (-a, -b), (-a, -c), (-d, -b), and (-d, -c)), after a 90-degree clockwise rotation, these points will move to new coordinates.

The general translation needed after a 90-degree rotation is to add the right amounts to the x and y coordinates to place it in Quadrant I. Typically, you will add positive values to the x and y coordinates.

If the rectangle is supposed to be moved from having its most negative x-coordinate to a positive x-coordinate and the most negative y-coordinate to a positive y-coordinate, you would do:

- Translate by (a, b), where 'a' is enough to make the x-coordinates positive and 'b' is enough to make the y-coordinates positive.

In the absence of specific coordinates for the rectangles, please replace 'a' and 'b' with the appropriate distances required for your specific rectangles.

So the answer would be: **translate by (a, b).**