Please answer the following equation.
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?
To rotate a point 90° clockwise, we can switch the x and y coordinates and then negate the new x coordinate.
The given line segment has endpoints (0, -3) and (0, -7).
Rotating the first endpoint (0, -3), we switch the x and y coordinates to get (-3, 0). Then, we negate the new x coordinate to get (3, 0).
Therefore, an endpoint of the rotated segment is (3, 0).
Rotate a point on a line at (−4, 6) 180° counterclockwise. What is the resulting point?
To rotate a point 180° counterclockwise, we can negate both the x and y coordinates of the point.
The given point is (-4, 6).
To rotate this point 180° counterclockwise, we negate the x and y coordinates:
New x coordinate = -(-4) = 4
New y coordinate = -(6) = -6
Therefore, the resulting point after rotating -4, 6 180° counterclockwise is (4, -6).
Jack discovers that the orientation of a triangle is counterclockwise. He then reflects the triangle over the y -axis. What is the orientation of the reflected figure?
When a figure is reflected over the y-axis, the orientation of the figure is reversed.
Since the original triangle had a counterclockwise orientation, reflecting it over the y-axis will result in a triangle with a clockwise orientation.