Question

A 90° counterclockwise rotation around the origin (O) transforms the vertices of the polygon TQRS. Given that the graph has X-coordinate marks -4, -2, 0, 2, 4, and Y-coordinate marks -4, -2, -1, 0, 2, 4, the coordinates of the transformed vertices are as follows:

a) Q' = (3, 1)
b) R' = (-3, 3)
c) S' = (-2, 0)
d) T' = (1, -2)

Answer 1

The original coordinates of the vertices T, Q, R, and S before the 90° counterclockwise rotation around the origin are as follows:
Original Q = (1, -3), Original R = (3, 3), Original S = (0, 2) and Original T = (2, 1)

Step-by-step explanation:

To solve this question, we need to understand the general rule for a 90° counterclockwise rotation around the origin (0,0) for any point (x,y). The rotation follows this rule:

If (x,y) is the point before rotation, then after a 90° counterclockwise rotation, the point will be at (-y, x).

Now, let's use this rule to find the original coordinates of the vertices T, Q, R, and S given their transformed coordinates after the rotation.

1. For Q', the coordinates after rotation are (3, 1). By using the rule, we know the original coordinates would be (-y, x). Swapping the positions and changing the sign of the second coordinate, we get:
Original Q = (1, -3)

2. For R', the coordinates after rotation are (-3, 3). Applying the rule (-y, x), we get:
Original R = (3, 3)

3. For S', the coordinates after rotation are (-2, 0). Again, applying the rule (-y, x), we find:
Original S = (0, 2)

4. For T', the coordinates after rotation are (1, -2). So, applying the rule (-y, x), we get:
Original T = (2, 1)

These are the original coordinates of the vertices T, Q, R, and S before the 90° counterclockwise rotation around the origin.