MATH SOLVE

4 months ago

Q:
# 50 points plzz helpp!!Triangle RED has vertices at (2, -2), (4,0), and the origin, respectively. Use rules of transformations to answer each of the items below. Be sure to answer in complete sentences, and when necessary, include your calculations.1. Model a scenario in which △RED is mapped onto its similar image △R'E'D' by an angle of rotation. In the model, describe the rotation as clockwise or counterclockwise, and include the angle of rotation.2.Use the model created in question #1 to name the coordinates of △R'E'D'. Include the mathematical steps taken in the transformation mapping △RED onto △R'E'D'.3. In two or more complete sentences, explain how undergoing an isometric transformation, such as an angular rotation, proves that △RED is similar to △R'E'D'.

Accepted Solution

A:

1) RED will be rotated 90° counterclockwise around the origin.

2) The coordinates of R'E'D' will be R'(2, 2); E'(0, 4) and F'(0, 0). The rule for a 90° counterclockwise rotation about the origin is that the coordinates (x, y) are mapped to (-y, x).

3) An isometric transformation is one in which the angles between sides and the distances of each side are preserved between the pre-image and the image. This means the angle measures and side lengths will be the same. Therefore the image will be similar to the pre-image, as the angle measures will be the same and the side lengths will be proportional.

2) The coordinates of R'E'D' will be R'(2, 2); E'(0, 4) and F'(0, 0). The rule for a 90° counterclockwise rotation about the origin is that the coordinates (x, y) are mapped to (-y, x).

3) An isometric transformation is one in which the angles between sides and the distances of each side are preserved between the pre-image and the image. This means the angle measures and side lengths will be the same. Therefore the image will be similar to the pre-image, as the angle measures will be the same and the side lengths will be proportional.