To find the dilation of a shape centered at the origin with a scale factor of 2, we will multiply each coordinate of the vertices by 2.
Given the points of the shape:
- \( a = (1, 4) \)
- \( b = (1, 1) \)
- \( c = (3, 1) \)
- \( d = (3, 4) \)
We apply the dilation formula for each point, which involves multiplying each coordinate by the dilation factor (2):
-
For point \( a \): \[ (1 \cdot 2, 4 \cdot 2) = (2, 8) \]
-
For point \( b \): \[ (1 \cdot 2, 1 \cdot 2) = (2, 2) \]
-
For point \( c \): \[ (3 \cdot 2, 1 \cdot 2) = (6, 2) \]
-
For point \( d \): \[ (3 \cdot 2, 4 \cdot 2) = (6, 8) \]
Thus, the dilated points are:
- \( a' = (2, 8) \)
- \( b' = (2, 2) \)
- \( c' = (6, 2) \)
- \( d' = (6, 8) \)
Therefore, the coordinates of the dilated shape are:
- \( (2, 8) \)
- \( (2, 2) \)
- \( (6, 2) \)
- \( (6, 8) \)
1 answer