Quadrant I Rectangle 1: (3, 4), (5, 4), (3, 8), (5, 8)
Quadrant II Rectangle 2: (-4, 1), (-6, 1), (-4, 5), (-6, 5)
Quadrant III Rectangle : (-1, -4), (-5, -4), (-1, 6), (-5, -6)
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 (blank)
To determine if the rectangle in Quadrant III is congruent to the rectangle in Quadrant I, the next step would be to translate the rotated rectangle horizontally to align with the coordinates of the rectangle in Quadrant III. The amount of the horizontal translation would depend on the difference in x-coordinates between the two rectangles.
so whats the answer?
To find the amount of horizontal translation needed to align the rotated rectangle in Quadrant III with the original rectangle in Quadrant I, we can compare the x-coordinates of corresponding points.
For the original rectangle in Quadrant I:
Point A: (3, 4)
Point B: (5, 4)
Point C: (3, 8)
Point D: (5, 8)
For the rotated rectangle in Quadrant III:
Point A': (-8, -3)
Point B': (-8, -5)
Point C': (-4, -3)
Point D': (-4, -5)
By comparing the x-coordinates of point A and A', we can see that the rotated rectangle needs to be horizontally translated by 11 units to align with the original rectangle. This means that the amount of horizontal translation needed is (11, 0).
Therefore, the next step would be to translate the rotated rectangle by (11, 0) horizontally to align it with the coordinates of the rectangle in Quadrant III.
thats wrong
My apologies for the incorrect response. Let's reevaluate the next step.
To determine if the rectangle in Quadrant III is congruent to the rectangle in Quadrant I, we can rotate the first rectangle 90 degrees clockwise about the origin to align it with Quadrant III. Let's perform that rotation:
The original rectangle in Quadrant I:
Point A: (3, 4)
Point B: (5, 4)
Point C: (3, 8)
Point D: (5, 8)
After rotating 90 degrees clockwise, the new coordinates of the rectangle points will be:
Point A': (4, -3)
Point B': (4, -5)
Point C': (8, -3)
Point D': (8, -5)
Now that we have the rotated rectangle in Quadrant III, the next step would be to translate it horizontally to align with the coordinates of the rectangle in Quadrant III. To find the horizontal translation amount, we can subtract the x-coordinate of Point A' from the x-coordinate of Point A:
Horizontal Translation = x-coordinate of Point A - x-coordinate of Point A'
= 3 - 4
= -1
Therefore, the next step would be to translate the rotated rectangle horizontally by -1 unit to align it with the coordinates of the rectangle in Quadrant III.