Question

Question successfully posted! Ask another 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? The points are : (-5,-4), (-1,-4) (-5,-6) and (-1,-6)
translate by (____)
(5,5) is not correct.

Answer 1

To determine the next step after rotating the rectangle in Quadrant III 90 degrees clockwise about the origin, we need to understand where the original points of the rectangle will end up after the rotation.

The original rectangle has vertices at the points:
- \((-5, -4)\)
- \((-1, -4)\)
- \((-5, -6)\)
- \((-1, -6)\)

After rotating each of these points 90 degrees clockwise about the origin:
- \((-5, -4)\) becomes \((-4, 5)\)
- \((-1, -4)\) becomes \((-4, 1)\)
- \((-5, -6)\) becomes \((-6, 5)\)
- \((-1, -6)\) becomes \((-6, 1)\)

So, the new points after rotation are:
- \((-4, 5)\)
- \((-4, 1)\)
- \((-6, 5)\)
- \((-6, 1)\)

Now, to translate this new rectangle in Quadrant II to be congruent to the rectangle in Quadrant I, you need to shift all the points to the right and up into Quadrant I.

To do this, you can translate by adding positive values to each coordinate. In particular, we can add \(6\) to the x-coordinates and \(6\) to the y-coordinates, which shifts all points to the right and upwards appropriately.

So, the translation vector would be \((6, 6)\).

Thus, the next step is to translate by \((6, 6)\).