what are points ABC after a rotation of 305 degrees clock wise?

Point A (2, 5)
Point B (5, 2)
Point C (2, 2)

Point A' (_,_)
Point B' (_,_)
Point C' (_,_)

3 answers

To find the new coordinates after a rotation of 305 degrees clockwise, we can use the rotation transformation formula:

x' = x*cos(theta) + y*sin(theta)
y' = -x*sin(theta) + y*cos(theta)

Let's apply this formula to each point:

For point A:
x' = 2*cos(305) + 5*sin(305) ≈ -2.572
y' = -2*sin(305) + 5*cos(305) ≈ 5.772

So, point A' is approximately (-2.572, 5.772).

For point B:
x' = 5*cos(305) + 2*sin(305) ≈ -1.828
y' = -5*sin(305) + 2*cos(305) ≈ 4.828

So, point B' is approximately (-1.828, 4.828).

For point C:
x' = 2*cos(305) + 2*sin(305) ≈ -0.414
y' = -2*sin(305) + 2*cos(305) ≈ 2.414

So, point C' is approximately (-0.414, 2.414).
Find the dilation of 0.25 with the center (0, 0) for the following points:
A (0, -3)
B (0, 2)

A' = __
B' = __
To find the dilation of 0.25 with the center (0, 0), we use the dilation transformation formula:

x' = k * x
y' = k * y

where k represents the scale factor, which is equal to 0.25 in this case.

For point A:
x' = 0.25 * 0 = 0
y' = 0.25 * (-3) = -0.75

So, point A' is (0, -0.75).

For point B:
x' = 0.25 * 0 = 0
y' = 0.25 * 2 = 0.5

So, point B' is (0, 0.5).