Question

After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(-3, 4), B'(-7, -1), and C'(-M1, 7). What are the coordinates of the vertices of the pre-image?

a. A(3, 4), B(1, 7), C(7, -M1)
b. A(4, -3), B(-1, -7), C(7, M1)
c. A(-4, 3), B(-1, -7), C(7, -M1)
d. A(4, 3), B(-1, 7), C(-7, M1)

Answer 1

The coordinates of the pre-image before the 90° rotation can be found by reversing the transformation. The original coordinates of A, B, and C are A(4, 3), B(-1, 7), and C(-7, M1), which corresponds to option d.

Step-by-step explanation:

To determine the coordinates of the vertices of the pre-image triangle before the 90° rotation around the origin, we need to apply the reverse process of the rotation transformation to the given coordinates of A'(-3, 4), B'(-7, -1), and C'(-M1, 7). When a point (x', y') is rotated 90° counterclockwise about the origin, the original coordinates can be found using the reverse transformation: x = y' and y = -x'. Applying this to the given points:

• For A'(-3, 4), the pre-image A would have the coordinates (4, 3).
• For B'(-7, -1), the pre-image B would have the coordinates (-1, 7).
• For C'(-M1, 7), the pre-image C would have the coordinates (7, M1).

Therefore, the correct answer is option d: A(4, 3), B(-1, 7), C(-7, M1).