where is point B (2, 1) after a translation of 5 units right, then 4 units up, followed by a rotation of 180 degrees around the origin
point B's final position is: ____
To find the final position of point B after the given transformations, we can go step by step.
1. Translation of 5 units right: Adding 5 to the x-coordinate of B, we get (2 + 5, 1) = (7, 1).
2. Translation of 4 units up: Adding 4 to the y-coordinate of the translated point B, we get (7, 1 + 4) = (7, 5).
3. Rotation of 180 degrees around the origin: For a point (x, y), the coordinates after a 180-degree rotation around the origin are (-x, -y). In this case, the coordinates after the rotation are (-7, -5).
Therefore, point B's final position is (-7, -5).
find the dilation of 2 for the given shape centered at the origin
A: (1, 4)
B: (1, 1)
C: (3, 1)
D: (3, 4)
A':
B':
C':
D':
To find the coordinates of the dilated points, we will multiply the x and y coordinates of each point by the dilation factor, which is 2 in this case.
A' = (2 * 1, 2 * 4) = (2, 8)
B' = (2 * 1, 2 * 1) = (2, 2)
C' = (2 * 3, 2 * 1) = (6, 2)
D' = (2 * 3, 2 * 4) = (6, 8)
Therefore, the coordinates of the dilated points are:
A': (2, 8)
B': (2, 2)
C': (6, 2)
D': (6, 8)
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 coordinates of the dilated points, we will multiply the x and y coordinates of each point by the dilation factor, which is 0.25 in this case.
A' = (0.25 * 0, 0.25 * -3) = (0, -0.75)
B' = (0.25 * 0, 0.25 * 2) = (0, 0.5)
Therefore, the coordinates of the dilated points are:
A': (0, -0.75)
B': (0, 0.5)