MATH SOLVE

3 months ago

Q:
# What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?

Accepted Solution

A:

A composite transformation is the production of the image of a figure through two or more transformationThe set of transformations that could be applied to rectangle ABCD to create rectangle A'B'C'D' is the second option;Reflected over the y-axis and rotated 180°The reason the above selected option is correct is as follows:Known parameters:The given coordinates of the vertices of the preimage of the rectangle ABCD are; A(-4, 2), B(-4, 1), C(-1, 1), and D(-1, 2)The given coordinates of the vertices of the image of the rectangle ABCD, which is rectangle A'B'C'D' are; A'(-4, -2), B'(-4, -1), C'(-1, -1), and D'(-1, -2)Solution:The form of the ordered pair of the vertices of the pre-image is negative value for x, positive value for y, which can be written as (-x, y), where x, and y, are positive numbersThe form of the ordered pair of the vertices of the image is (-x, -y)The location of a point (-x, y) following a reflection over the y-axis is the point (x, y)The location of a point (x, y) following a 180° rotation is the point (-x, -y)Therefore, the set of transformations that can be applied to (-x, y), to create (-x, -y), is a reflection over the y-axis, followed by a rotation of 180Which gives;The set of transformations that transforms A(-4, 2) to create A'(-4, -2), B(-4, 1), to create B'(-4, -1), C(-1, 1), to create C'(-1, 1), and D(-1, 2), to create D'(-1, -2) is a reflection over the y-axis followed by a rotation of 180°.Therefore, the correct option is; Reflected over the y-axis and rotated 180°Learn more about composite transformations here: