Given a point x,y , what is the new point when it is rotated counterclockwise 270 degrees
To rotate a point (x, y) counterclockwise by 270 degrees, we can use the following rotation matrix formula:
new_x = x*cos(270) - y*sin(270)
new_y = x*sin(270) + y*cos(270)
Since cos(270) = 0 and sin(270) = -1, the formulas simplify to:
new_x = -y
new_y = x
Therefore, the new point will be (-y, x).
Nope it was y,-x
Apologies for the mistake. You are correct.
When a point (x, y) is rotated counterclockwise by 270 degrees, the new point becomes (y, -x).
Thank you for pointing out the error.
Ye
If you have any more questions or need further clarification, feel free to ask! I'm here to help.
Rotate a point 1,2 by 90 degrees
To rotate a point (1, 2) counterclockwise by 90 degrees, we can use the rotation matrix formula:
new_x = x*cos(90) - y*sin(90)
new_y = x*sin(90) + y*cos(90)
Since cos(90) = 0 and sin(90) = 1, the formulas simplify to:
new_x = -y
new_y = x
Plugging in the values (1, 2) for x and y:
new_x = -2
new_y = 1
Therefore, the new point after rotating (1, 2) counterclockwise by 90 degrees is (-2, 1).
Also remember this please:
X,Y rotated counterclockwise by 270 degrees is y,-x.
Doing the same but rotating it clockwise makes it -y,x. Got that?
Got it! Thank you for the reminder.
When a point (x, y) is rotated counterclockwise by 270 degrees, the new point becomes (y, -x).
When a point (x, y) is rotated clockwise by 270 degrees, the new point becomes (-y, x).
I will keep this in mind for future reference. If you have any more questions or need assistance, feel free to ask.