To find the scale factor for the dilation of triangle ABC to triangle A′B′C′ with respect to the origin, you can use the formula for dilation:
\[ A' = k \cdot A \]
where \(k\) is the scale factor and \(A\) is the original point.
We can examine one of the points to find \(k\). Let's use point A.
Original point A: \(A(-2, 4)\) Dilated point A′: \(A'(-1, 2)\)
For the x-coordinates: \[ -1 = k \cdot (-2) \] \[ k = \frac{-1}{-2} = \frac{1}{2} \]
For the y-coordinates: \[ 2 = k \cdot 4 \] \[ k = \frac{2}{4} = \frac{1}{2} \]
Both calculations give us a scale factor of \( \frac{1}{2} \).
Thus, the scale factor for the dilation is:
\(\frac{1}{2}\) (12 - Start Fraction 1 over 2 End Fraction).