The first step to determine that the triangle in the quadrant III is congruent to the rectangle in the quadrant I was to rotate the first rectangle 90° clockwise about the origin what is the first step? what do you Translate by?

Answer 1

To rotate the first rectangle 90° clockwise about the origin, the first step is to establish the coordinates of the vertices of the rectangle in quadrant I. Let's assume the rectangle has vertices A, B, C, and D.

Next, we need to determine the coordinates of the corresponding vertices when the rectangle is rotated 90° clockwise. To do this, we can use the rule for rotating points in the coordinate plane:

For a point (x, y) rotated 90° clockwise, the new coordinates will be (-y, x).

Applying this rule to each vertex of the rectangle, we get the following:

- Vertex A: The coordinates for A in quadrant I remain the same.
- Vertex B: The coordinates for B become (-y, x).
- Vertex C: The coordinates for C become (-y, x).
- Vertex D: The coordinates for D become (-y, x).

By translating the rectangle by the new coordinates for vertices B, C, and D, we can determine the position of the triangle in quadrant III.