graph 2,1 270 degrees clockwise about the origin
To graph the point (2,1) rotated 270 degrees clockwise about the origin, we need to calculate the new coordinates.
Let's first plot the original point (2,1) on the coordinate plane.
Now, let's think about a point (x, y) located 270 degrees clockwise from (2,1) about the origin. To rotate a point 270 degrees clockwise, we can find the new coordinates (x', y') using the following formulas:
x' = x * cos(270) - y * sin(270)
y' = x * sin(270) + y * cos(270)
Since the origin is (0, 0), we have x = 2 and y = 1. Plugging these values into the formulas, we get:
x' = 2 * cos(270) - 1 * sin(270)
= 2 * 0 - 1 * (-1)
= 0 + 1
= 1
y' = 2 * sin(270) + 1 * cos(270)
= 2 * (-1) + 1 * 0
= -2 + 0
= -2
Therefore, the new coordinates of the point (2,1) rotated 270 degrees clockwise about the origin are (1, -2).
Plotting this new point on the graph, we can see that it is located below and to the left of the original point.