Question

The vertices of a rectangle are M(-5, -5), N(-1, -5), O(-1, 1), and P(-5, 1). A rotation about the origin maps P to the point (1, 5). What are the coordinates of point N after the rotation?

A) (1, 5)
B) (-5, -1)
C) (5, 1)
D) (-1, -5)

Answer 1

After a 90-degree rotation counterclockwise of the rectangle, point N with original coordinates (-1, -5) will have new coordinates (5, 1).

Step-by-step explanation:

The student is asking about the coordinates of point N after a rotation of a rectangle around the origin. Since point P is rotated to (1, 5), we can infer that this is a 90-degree rotation counterclockwise. To find out the new coordinates of point N, we need to apply the similar rotation to it.

The original coordinates of point N are (-1, -5). A 90-degree rotation counterclockwise transforms a point (x, y) to (-y, x). So, if we apply this to point N:

• First coordinate (x): -(-5) = 5
• Second coordinate (y): -1

After the rotation, point N will be at (5, 1).

Therefore, the coordinates of point N after the rotation are (5, 1).