Rotate the point (5,8) on a geometric figure 270 degree clockwise. What is the new point
To rotate a point (x,y) 270 degrees clockwise, we can use the following formulas:
x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)
In this case, the given point is (5,8) and the angle of rotation is 270 degrees clockwise.
We can convert 270 degrees to radians by multiplying by (π/180):
270 degrees * (π/180) = 3π/2 radians
Using the formulas above, we can calculate the new coordinates:
x' = 5*cos(3π/2) - 8*sin(3π/2)
= 5*0 - 8*(-1)
= 0 + 8
= 8
y' = 5*sin(3π/2) + 8*cos(3π/2)
= 5*(-1) + 8*0
= -5 + 0
= -5
Therefore, the new point after rotating (5,8) 270 degrees clockwise is (8,-5).
To rotate a point 270 degrees clockwise, we need to apply the following formulas:
NewX = (OldX * cos(angle)) - (OldY * sin(angle))
NewY = (OldX * sin(angle)) + (OldY * cos(angle))
Let's substitute the old coordinates into these formulas:
OldX = 5
OldY = 8
Angle = -270 degrees (negative because we are rotating clockwise)
NewX = (5 * cos(-270)) - (8 * sin(-270))
= (5 * 0) - (8 * -1)
= 0 + 8
= 8
NewY = (5 * sin(-270)) + (8 * cos(-270))
= (5 * -1) + (8 * 0)
= -5 + 0
= -5
Therefore, the new point after rotating (5,8) 270 degrees clockwise is (8,-5).