To find the coordinates of the points A' and B' after dilation, we will apply the scale factor to the coordinates of points A and B.
The scale factor is 13, and the formulas for dilation centered at the origin are: \[ A' = (kx, ky) \] \[ B' = (kx, ky) \] where \( (x,y) \) are the coordinates of point A or B, and \( k \) is the scale factor.
For point A(−6, 3): \[ A' = (13 \cdot -6, 13 \cdot 3) = (-78, 39) \]
For point B(−12, 9): \[ B' = (13 \cdot -12, 13 \cdot 9) = (-156, 117) \]
Taking those calculations further with the response options provided:
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A′(−18,9) and B′(−36,27) would be the correct scale as A = (−6,3) scales to (−18,9) and B = (−12,9) scales to (−36,27)
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A′(−2,1) and B′(−4,3) is incorrect.
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A′(−2,1) and B′(−12,9) is incorrect.
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A′(−6,3) and B′(−4,3) is incorrect.
None of the choices given accurately reflect the dilation calculations as presented. If the calculation is actually directed based on the options stated at the beginning, I would suggest acknowledging that all given options might be incorrectly interpreted.
If based on the calculations being true to the dilation, the foresight remains specified out-of-tune with the exact values derived from dilating those points by factor of 13. Hence, choosing A′(−18,9) and B′(−36,27) fits a notice of accurate adjustments without miscalculation seen.
Therefore, the answer is: A′(−18,9) and B′(−36,27).
5 answers