Question

The image is a scatter chart representing data points plotted on a Cartesian coordinate system. The vertical axis (y-axis) ranges from 1 to 8, while the horizontal axis (x-axis) goes from -9 to 9. The chart includes numerical values and appears to display relationships or distributions between the plotted points, possibly reflecting trends or patterns in the dataset.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?

Answer 1

After rotating the rectangle in Quadrant III by 90 degrees clockwise about the origin, the next step to demonstrate that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I is to compare the dimensions of both rectangles.

To do this, follow these steps:

1. Identify the vertices of both rectangles: Calculate the coordinates of the corners of the original rectangle in Quadrant III and the rotated rectangle in Quadrant I. This will help you visualize their locations and dimensions.

2. Measure the sides of the rectangles: Determine the lengths of the sides of both rectangles. Since rotating does not change side lengths, if the lengths are the same, then the rectangles are congruent.

3. Check for angles: Verify that the angles in both rectangles are right angles (90 degrees) to confirm they are both rectangles.

4. Conclude congruence: If both the lengths of the sides and the angles are confirmed to be the same, you can conclude that the rectangle in Quadrant III is congruent to the rectangle in Quadrant I.

This analytical approach will solidify your claim of congruence following the rotation.