To find the coordinates of the points after a dilation with a scale factor of 3 from the origin, we can use the formula for dilation. Given a point \((x, y)\) and a scale factor \(k\), the new coordinates \((x', y')\) after dilation are given by:
\[ x' = k \cdot x \] \[ y' = k \cdot y \]
In this case, the scale factor \(k = 3\).
Now applying this to each vertex:
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For point \(A(-2, -2)\): \[ A' = (3 \cdot -2, 3 \cdot -2) = (-6, -6) \]
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For point \(B(-4, -3)\): \[ B' = (3 \cdot -4, 3 \cdot -3) = (-12, -9) \]
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For point \(C(-2, -5)\): \[ C' = (3 \cdot -2, 3 \cdot -5) = (-6, -15) \]
After calculating all points, we find:
- \(A' = (-6, -6)\)
- \(B' = (-12, -9)\)
- \(C' = (-6, -15)\)
Thus, the final coordinates after dilation are:
- A′ = (-6, -6)
- B′ = (-12, -9)
- C′ = (-6, -15)