give a point (x, y) on a geometric figure, what is the new point when the figure is rotated counterclockwise about the origin 180 degrees?
If a point (x, y) is on a geometric figure and the figure is rotated counterclockwise about the origin by 180 degrees, the new point would be (-x, -y). This is because rotating a point 180 degrees around the origin is equivalent to reflecting the point over both the x-axis and the y-axis.
give a point (1, 2) on a geometric figure, what is the new point when the figure is rotated clockwise about the origin 180 degrees?
If a point (1, 2) is on a geometric figure and the figure is rotated clockwise about the origin by 180 degrees, the new point would be (-1, -2). This is because rotating a point 180 degrees around the origin is equivalent to reflecting the point over both the x-axis and the y-axis, resulting in the coordinates being negated.
give a point (-6, 4) on a line segment, what is the new line segment when the figure is rotated counterclockwise about the origin 180 degrees?
When a point on a line segment is rotated counterclockwise 180 degrees around the origin, the resulting point will be the reflection of the original point over the origin.
Given the point (-6, 4), the new point after a 180-degree counterclockwise rotation around the origin would be (6, -4). This is because the x-coordinate changes sign from negative to positive, and the y-coordinate changes sign from positive to negative, reflecting the point over the origin.
Therefore, the new line segment would be the segment connecting the original point (-6, 4) and the new point (6, -4).
given point A(2,6) on the triangle, where would the new point on the triangle be after a rotation of 90 degrees counterclockwise
To find the new point on the triangle after a rotation of 90 degrees counterclockwise from point A(2,6), we can use the following rotation formula:
For a 90-degree counterclockwise rotation around the origin:
New_x = -y
New_y = x
Given point A(2,6):
New_x = -6 = -6
New_y = 2
Therefore, the new point after a 90-degree counterclockwise rotation from point A(2,6) would be at (-6, 2).