MATH SOLVE

5 months ago

Q:
# Rectangle DEFG has vertices D(-6, -5) E(-6 -2) F(-2, -2) G(-2, -5). The figure is first translated 3 units up and then rotated 90° about the origin. What is the shape of the figure after this sequence of transformations?

Accepted Solution

A:

Given rectangle DEFG has vertices D(-6, -5) E(-6 -2) F(-2, -2) G(-2, -5).

Translation of rectangle DEFG by 3 units up will result in an image with the same x-coordinate and a y-coordinate obtained by adding 3 to the y-cordinates of the vertices of DEFG.

Thus a translation of 3 units up will result in rectangle D'E'F'G' with vertices D'(-6, -2), E'(-6, 1), F'(-2, 1), G'(-2, -2).

Assuming the rotation of 90° about the origin was done in the clockwise direction, this will result in an image having the verties obtained by interchanging the x-coordinate and the y-coordinate of the vertices of D'E'F'G' and then the sign of the y-coordinate is changed.

Thus, a rotation of 90° about the origin in the clockwise direction will result in the rectangle D"E"F"G" with vertices D"(-2, 6), E"(1, 6), F"(1, 2), G"(-2, 2).

Therefore, if rectangle DEFG with vertices D(-6, -5) E(-6 -2) F(-2, -2) G(-2, -5) is first translated 3 units up and then rotated 90° about the origin, the shape of the figure formed after this sequence of transformations is a rectangle with vertices D"(-2, 6), E"(1, 6), F"(1, 2), G"(-2, 2).

Translation of rectangle DEFG by 3 units up will result in an image with the same x-coordinate and a y-coordinate obtained by adding 3 to the y-cordinates of the vertices of DEFG.

Thus a translation of 3 units up will result in rectangle D'E'F'G' with vertices D'(-6, -2), E'(-6, 1), F'(-2, 1), G'(-2, -2).

Assuming the rotation of 90° about the origin was done in the clockwise direction, this will result in an image having the verties obtained by interchanging the x-coordinate and the y-coordinate of the vertices of D'E'F'G' and then the sign of the y-coordinate is changed.

Thus, a rotation of 90° about the origin in the clockwise direction will result in the rectangle D"E"F"G" with vertices D"(-2, 6), E"(1, 6), F"(1, 2), G"(-2, 2).

Therefore, if rectangle DEFG with vertices D(-6, -5) E(-6 -2) F(-2, -2) G(-2, -5) is first translated 3 units up and then rotated 90° about the origin, the shape of the figure formed after this sequence of transformations is a rectangle with vertices D"(-2, 6), E"(1, 6), F"(1, 2), G"(-2, 2).