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 (_)
The next step is to translate the rectangle by a certain amount. However, the question does not provide the amount or direction of the translation, so it is not possible to determine the next step with the given information.
If the given coordinates (-5,-4), (-1,-4), (-5,-6), (-1,-6) represent the vertices of a rectangle in Quadrant III, to determine that it is congruent to the rectangle in Quadrant I after rotating it 90 degrees clockwise about the origin, the next step would be to translate the rectangle.
To find the translation vector, you can compare the corresponding vertices of the two rectangles. As the rectangle in Quadrant III is the result of rotating the rectangle in Quadrant I 90 degrees clockwise, the corresponding vertices will have the same distances from the origin but opposite signs.
For example, comparing the bottom left vertices (-5,-6) and (-6, -5), you can see that the x-coordinate increases by 1 (from -5 to -4), and the y-coordinate increases by 1 (from -6 to -5). Therefore, the translation vector would be (1,1).
To translate the rectangle in Quadrant III by (1,1), you would add 1 to the x-coordinate and 1 to the y-coordinate of each vertex.
The new vertices of the translated rectangle would be:
(-4,-3), (0,-3), (-4,-5), (0,-5)
translate by (_)
To determine the translation amount, we need to compare the corresponding vertices of the two rectangles. As we don't have that information, it is not possible to determine the translation by (_).
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 (_)
info: (-5,-4) (-1,-4) (-5,-6) (-1,-6)
To determine the translation step, we can compare the corresponding vertices of the two rectangles. After rotating the rectangle in Quadrant III 90 degrees clockwise about the origin, we can observe that the bottom-left vertex (-5,-6) will have coordinates (-6, -5) in Quadrant I.
To find the translation vector, we can subtract the coordinates of the corresponding vertices in Quadrant I from those in Quadrant III. By subtracting (-6, -5) from (-5, -6), we get a translation vector of (1, -1).
Therefore, the next step is to translate the rectangle in Quadrant III by moving each of its vertices one unit to the right and one unit downwards.
The new coordinates of the translated rectangle would be:
(-4, -5), (0, -5), (-4, -7), (0, -7)