Question

a line segment has endpoints (2,-1) and 5,-4). what are the new endpoints after rotating the segment 90 degrees

Answer 1

To rotate a line segment 90 degrees counterclockwise, you can use the following formula:

(x', y') = (-y, x)

where (x', y') are the new coordinates, and (x, y) are the original coordinates.

Let's calculate the new endpoints:
1. For the first endpoint (2, -1):
Applying the formula, we have:
x' = -(-1) = 1
y' = 2

Therefore, the new endpoint is (1, 2).

2. For the second endpoint (5, -4):
Applying the formula, we have:
x' = -(-4) = 4
y' = 5

Therefore, the new endpoint is (4, 5).

Hence, after rotating the line segment 90 degrees counterclockwise, the new endpoints are (1, 2) and (4, 5).