Demonstrating the properties of rotations, if a line segment with endpoints (0,−3)

Question

and (0,−7)
is rotated 90°
clockwise, what is an endpoint of this rotated segment?(1 point)
Responses

(−3, 0)

(0, 7)

(0, 3)

(3, 0)

Answer 1

To find the new coordinates of the endpoints after a 90° clockwise rotation, we can use the rotation transformation formulas.

For a point \((x, y)\), after a 90° clockwise rotation, the new coordinates \((x', y')\) can be calculated as: \[ x' = y \] \[ y' = -x \]

Let's apply this to the endpoint \((0, -3)\):

1. The original coordinates are \(x = 0\) and \(y = -3\).
2. Applying the transformation: \[ x' = y = -3 \] \[ y' = -x = -0 = 0 \]

So, the new coordinates of the point \((0, -3)\) after a 90° clockwise rotation are \((-3, 0)\).

Now, let's also check the other endpoint \((0, -7)\):

1. The original coordinates are \(x = 0\) and \(y = -7\).
2. Applying the transformation: \[ x' = y = -7 \] \[ y' = -x = -0 = 0 \]

So, the new coordinates of the point \((0, -7)\) after a 90° clockwise rotation are \((-7, 0)\).

Therefore, the endpoints of the segment after a 90° clockwise rotation will be:

1. From \((0, -3)\) to \((-3, 0)\)
2. From \((0, -7)\) to \((-7, 0)\)

Since the question asks for one of the endpoints after rotation, the answer is: \((-3, 0)\).