Given the following points determine whether the transformation was a Rotation(specify direction and size), a reflection(over what point/line) or trasnlation(specify the rule).
1.
C(0,4). C'(2,6) N(-2,3) N'(0,5)
2.
G(0,0) G'(4,0) R(-1,4) R'(5,4)
3.
K(-4,-2) K'(4,-2) V(1,1) V'(9,1)
To determine whether a transformation is a rotation, reflection, or translation, you need to analyze the changes in the coordinates of the points.
1. C(0,4), C'(2,6), N(-2,3), N'(0,5)
- To analyze the transformation, first, calculate the changes in the x-coordinates and y-coordinates.
Delta x = x'-x
Delta y = y'-y
For C: Delta x = 2-0 = 2, Delta y = 6-4 = 2
For N: Delta x = 0-(-2) = 2, Delta y = 5-3 = 2
Since the changes in both x-coordinates and y-coordinates are the same, we can conclude that the transformation is a translation.
Translation rule: Δx = 2, Δy = 2
2. G(0,0), G'(4,0), R(-1,4), R'(5,4)
- Calculate the changes in the x-coordinates and y-coordinates.
For G: Delta x = 4-0 = 4, Delta y = 0-0 = 0
For R: Delta x = 5-(-1) = 6, Delta y = 4-4 = 0
Since the changes in the y-coordinates are zero (meaning no vertical change), and the changes in the x-coordinates are the same, we can conclude that the transformation is a translation.
Translation rule: Δx = 4, Δy = 0
3. K(-4,-2), K'(4,-2), V(1,1), V'(9,1)
- Calculate the changes in the x-coordinates and y-coordinates.
For K: Delta x = 4-(-4) = 8, Delta y = -2-(-2) = 0
For V: Delta x = 9-1 = 8, Delta y = 1-1 = 0
Since the changes in the y-coordinates are zero (meaning no vertical change), and the changes in the x-coordinates are the same, we can conclude that the transformation is a translation.
Translation rule: Δx = 8, Δy = 0
In all three cases, the transformations are translations with the indicated translation rules.