To find the coordinates of points \( A' \) and \( B' \) after a dilation with a scale factor of 2 and with the center of dilation at the origin, we can use the formula for dilation:
\[ A' = (k \cdot x_A, k \cdot y_A) \] \[ B' = (k \cdot x_B, k \cdot y_B) \] where \( k \) is the scale factor, and \((x_A, y_A)\) and \((x_B, y_B)\) are the coordinates of points \( A \) and \( B \).
Given:
- Point \( A(-4, 1) \)
- Point \( B(-1, 3) \)
- Scale factor \( k = 2 \)
Now, we will apply the dilation to both points:
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For Point A: \[ A' = (2 \cdot -4, 2 \cdot 1) = (-8, 2) \]
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For Point B: \[ B' = (2 \cdot -1, 2 \cdot 3) = (-2, 6) \]
Thus, the coordinates after the dilation are:
- \( A'(-8, 2) \)
- \( B'(-2, 6) \)
Therefore, the coordinates of points \( A' \) and \( B' \) after the dilation are:
- \( A'(-8, 2) \)
- \( B'(-2, 6) \)
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