Question

Parallelogram ABCD is rotated 45° counterclockwise using the origin as the center of rotation. On a coordinate plane, parallelogram A B C D has points (2, 5), (2, 2), (negative 1, negative 1), (negative 1, 2). Which graph shows the image of ABCD? On a coordinate plane, parallelogram A prime B prime C prime D prime has points (negative 2, 5), (0, 3), (0, negative 1.2), (negative 2, 1). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (negative 2, 5), (negative 2, 1), (0, negative 1), (0, 3). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (5, 2), (3, 0), (negative 1.5, 0), (0.5, 2). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (5, 2), (1, 2), (negative 1.5, 0), (2.8, 0).

Answer 1

9514 1404 393

Answer:

A. On a coordinate plane, parallelogram A'B'C'D' has points (-2, 5), (0, 3), (0, -1.2), (-2, 1)

Explanation:

None of the choices are very good matches to the actual coordinates. Rounded to tenths, they should be ...

A'(-2.1, 5.0), B'(0, 2.8), C'(0, -1.4), D'(-2.1, 0.7)

The closest match is choice A.

_____

The transformation is ...

(x, y) ⇒ (0.71x -0.71y, 0.71x +0.71y)

where 0.71 is an approximation of √2/2.

9514 1404 393 Answer: A. On a coordinate plane, parallelogram - 1

Answer 2

9514 1404 393

Answer:

A. On a coordinate plane, parallelogram A'B'C'D' has points (-2, 5), (0, 3), (0, -1.2), (-2, 1)

Explanation:

None of the choices are very good matches to the actual coordinates. Rounded to tenths, they should be ...

A'(-2.1, 5.0), B'(0, 2.8), C'(0, -1.4), D'(-2.1, 0.7)

The closest match is choice A.

_____

The transformation is ...

(x, y) ⇒ (0.71x -0.71y, 0.71x +0.71y)

where 0.71 is an approximation of √2/2.