Graphically:
Measure the distance from each point ot the centre of rotation and continue to the other side. This is easiest done by measuring the x and y distances separately; they swap sides of the point: left ←→ right, above ←→ below. eg:
A triangle ABC {(1,1), (3,4), (2,1)} rotated 180° about point (2, 2):
! (1, 1):
x distance is 2 - 1 = 1 to left of centre, so new x is to right at 2 + 1 = 3
y distance is 2 - 1 = 1 below centre, so new y is above at 2 + 1 = 3
→ A' is (3, 3)
B (3, 4)
x distance is 3 - 2 = 1 to right of centre, so new x is to left at 2 - 1 = 1
y distance is 4 - 2 = 2 above centre, so new y is below at 2 - 2 = 0
→ B' is (1, 0)
C (2, 1)
x distance is 2 - 2 = 0 on the centre, so new x is also on the centre at 2 + 0 = 2
y distance is 2 - 1 = 1 below centre, so new y is above at 2 + 1 = 3
→ C' is (2, 3)
Thus triangle ABC {(1,1), (3,4), (2,1)} goes to triangle A'B'C' {(3,3), (1,0), (2,3)} when rotated 180° about centre (2,2).
Algebraically:
Rotating 180° about point (x0, y0):
point (x, y) → (2 x0 - x, 2 y0 - y)
For triangle ABC {(1,1), (3,4), (2,1)} rotated 180° about point (2, 2):
A': (2×2 - 1, 2×2 - 1) = (3, 3)
B': (2×2 - 3, 2×2 - 4) = (1, 0)
C': (2×2 - 2, 2×2 - 1) = (2, 3)
ie ABC → A'B'C {(3,3), (1,0), (2,3)} [as before].
The same as 180 degrees clockwise. What do you mean "the answer to"?
Change the sign: from + to - or - to +
translation: is a slide reflection : is a flip roation: you rotate the triganle around like 180 degrees
True
When you rotate it around a point found in the middle of the figure 180 degrees. For example, H does have rotational symmetry however, E doesn't
The same as 180 degrees clockwise. What do you mean "the answer to"?
To rotate a figure 180 degrees clockwise about the origin you need to take all of the coordinates of the figure and change the sign of the x-coordinates to the opposite sign(positive to negative or negative to positive). You then do the same with the y-coordinates and plot the resulting coordinates to get your rotated figure.
Yes, the screen will rotate 180 degrees.
To rotate a figure 180 degrees clockwise, you can achieve this by first reflecting the figure over the y-axis and then reflecting it over the x-axis. This double reflection effectively rotates the figure 180 degrees clockwise around the origin.
Negate each of the x and y components of all three vertices of the triangle. For example, a triangle with vertices (1,2), (8,3), and (5,6) would become (-1,-2), (-8,-3) and (-5,-6) when rotated 180 degrees about the origin.
Change the sign: from + to - or - to +
A 1/2 rotation
A horse can rotate its ears as far as 180 degrees.
180 degrees
Visualize a capital "N." Rotated 90 degrees counter-clockwise (a quarter turn to the left) it would look like a capital "Z."
a mirror?
It rotates 90 degrees.