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? fill in the blank
translate by (_)
Quadrant I: (8,3) (4,3) (8,5) (4,5)
Quadrant III: (-5,-4) (-5,-6) (-1,-4) (-1,-6)
The next step is to translate the rectangle by ________.
To determine the translation needed, we can observe that the x-coordinates of corresponding points between the rectangles have a difference of 13 (8 - (-5) = 13), and the y-coordinates have a difference of -1 (3 - (-4) = -1).
Therefore, the translation required to move the rectangle in Quadrant III to coincide with the rectangle in Quadrant I is by (-13, 1).
didnt work
I apologize for the previous response. Let's correct it.
To determine the translation needed, we can observe that the x-coordinates of corresponding points between the rectangles have a difference of 13 (-5 - 8 = -13), and the y-coordinates have a difference of 9 (-4 - 3 = -7).
Therefore, the translation required to move the rectangle in Quadrant III to coincide with the rectangle in Quadrant I is by (-13, -7).
nope still wrong
Apologies for the confusion. Let's try a different approach.
To determine the translation needed, we can observe that the x-coordinates of corresponding points between the rectangles have a difference of 13 (-5 - 8 = -13), and the y-coordinates have a difference of -9 (-4 - 3 = -7).
However, since the translation is from Quadrant III to Quadrant I, we need to take into account that the x-axis is flipped. So, the x-coordinate difference becomes positive. Therefore, the translation required to move the rectangle in Quadrant III to coincide with the rectangle in Quadrant I is by (13, -7).
none of the answers are working is there another way to find the answer
I apologize for the confusion. Let's try another approach to determine the correct translation.
To find the correct translation, we can use the properties of congruent shapes. Since the two rectangles are congruent, the corresponding sides of the rectangles should have the same lengths.
Let's consider the length of the side from (8,3) to (4,3) in Quadrant I. The length of this side is 4 units.
Now, let's consider the length of the corresponding side in Quadrant III, which is from (-5,-4) to (-1,-4). The length of this side is also 4 units.
This shows that the rectangle in Quadrant III is horizontally congruent to the rectangle in Quadrant I. We can conclude that the translation needed to align these rectangles is purely horizontal.
To move the rectangle in Quadrant III to coincide with the rectangle in Quadrant I, we need to translate it horizontally by the difference in x-coordinates. In this case, the difference is -13 units. Therefore, the correct translation for the rectangle in Quadrant III is to translate it horizontally by (-13, 0).