To find the coordinates of the new vertices X′, Y′, and Z′ after the dilation, we will use the formula for dilation about the origin:
\[ (X', Y') = (k \cdot X, k \cdot Y) \]
where \( k \) is the scale factor, and \( (X, Y) \) are the original coordinates of the point.
The given scale factor is \( k = 12 \).
The original coordinates provided are:
- X(2, 4)
- Y(6, 0)
- Z(7, 2)
Now we calculate the new coordinates for each vertex:
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For X(2, 4): \[ X' = (12 \cdot 2, 12 \cdot 4) = (24, 48) \]
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For Y(6, 0): \[ Y' = (12 \cdot 6, 12 \cdot 0) = (72, 0) \]
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For Z(7, 2): \[ Z' = (12 \cdot 7, 12 \cdot 2) = (84, 24) \]
So, the coordinates of the new vertices after dilation are:
- \( X' = (24, 48) \)
- \( Y' = (72, 0) \)
- \( Z' = (84, 24) \)
Looking at the responses you provided, it seems that none of them correctly matches the calculated coordinates. Therefore, there might have been a mistake in understanding the original triangle coordinates, or those responses may not pertain to the problem stated.
Please ensure that the original triangle vertices are as follows or check for any updates:
- X(2, 4)
- Y(6, 0)
- Z(7, 2)
If so, then the coordinates after dilation are \( X'(24, 48), Y'(72, 0), Z'(84, 24) \). If the original points differ, please provide them for accurate calculations.
3 answers