Question

Demonstrating the properties of rotations, if a line segment with endpoints (0,−3) and (0,−7) is rotated 90° clockwise, what is an endpoint of this rotated segment?
1. Responses (0, 7)
2. parenthesis (0, 3)
3. parenthesis (−3, 0)
4. parenthesis (3, 0)

Answer 1

To determine the new endpoint of the line segment after a 90° clockwise rotation, we can use the rotation rules in the Cartesian coordinate system.

The original endpoints of the segment are:
- A (0, -3)
- B (0, -7)

We will apply the 90° clockwise rotation transformation to point A first (0, -3).

The general formula for a 90° clockwise rotation of a point (x, y) is:
\[
(x', y') = (y, -x)
\]

For point A (0, -3):
\[
x' = -3 \quad (y)
\]
\[
y' = 0 \quad (-x)
\]

Thus, the new coordinates of point A after rotation are:
\[
( -3, 0 )
\]

Now, let's apply the same transformation to point B (0, -7):

For point B (0, -7):
\[
x' = -7 \quad (y)
\]
\[
y' = 0 \quad (-x)
\]

Thus, the new coordinates for point B after rotation are:
\[
( -7, 0 )
\]

Now, we can examine the given response choices for an endpoint of this rotated segment:
1. (0, 7)
2. (0, 3)
3. (-3, 0)
4. (3, 0)

From our calculations, the endpoint we found from point A is (-3, 0). Therefore, the correct answer is:

**3. (−3, 0)**