Quadrilateral ABCD has vertices A (2,4), B (2,1), C (4,1), and D (4,5). A'B'C'D' is a dilation about the origin with a scale factor of 0.5.
What are the coordinates of A', B', C', and D'?
To find the coordinates of A', B', C', and D', we need to apply the dilation transformation to the original coordinates of A, B, C, and D.
The dilation transformation is given by the formula:
(x', y') = (k * x, k * y)
Where:
- (x', y') are the coordinates of the point after dilation,
- (x, y) are the original coordinates of the point,
- k is the scale factor.
Given that the scale factor is 0.5, we can calculate the coordinates of A', B', C', and D' as follows:
For point A:
x' = (0.5) * 2 = 1
y' = (0.5) * 4 = 2
So, A' is located at (1, 2).
For point B:
x' = (0.5) * 2 = 1
y' = (0.5) * 1 = 0.5
So, B' is located at (1, 0.5).
For point C:
x' = (0.5) * 4 = 2
y' = (0.5) * 1 = 0.5
So, C' is located at (2, 0.5).
For point D:
x' = (0.5) * 4 = 2
y' = (0.5) * 5 = 2.5
So, D' is located at (2, 2.5).
Therefore, the coordinates of A', B', C' and D' are as follows:
A' (1, 2)
B' (1, 0.5)
C' (2, 0.5)
D' (2, 2.5)
To find the coordinates of A', B', C', and D', we need to apply the dilation transformation to the original coordinates of A, B, C, and D.
The dilation transformation scales the coordinates by a given scale factor. In this case, the scale factor is 0.5.
To apply the dilation, multiply the x and y coordinates of each point by the scale factor.
Coordinates of A':
x-coordinate: 2 * 0.5 = 1
y-coordinate: 4 * 0.5 = 2
Therefore, A' has coordinates (1, 2).
Coordinates of B':
x-coordinate: 2 * 0.5 = 1
y-coordinate: 1 * 0.5 = 0.5
Therefore, B' has coordinates (1, 0.5).
Coordinates of C':
x-coordinate: 4 * 0.5 = 2
y-coordinate: 1 * 0.5 = 0.5
Therefore, C' has coordinates (2, 0.5).
Coordinates of D':
x-coordinate: 4 * 0.5 = 2
y-coordinate: 5 * 0.5 = 2.5
Therefore, D' has coordinates (2, 2.5).
In summary, the coordinates of A', B', C', and D' are A' (1, 2), B' (1, 0.5), C' (2, 0.5), and D' (2, 2.5).