Question

estimation without doing calculations, use side de and side de to estimate the scale factor for the dilation shown. then use two corresponding sides to find the scale factor.
side de looks about 2 times longer than side de.
the scale factor for this dilation is
(simplify your answer.)

Explanation:

Step1: Identify lengths of sides

From the grid, side DE spans from $x=0$ to $x=4$, so $DE = 4$. Side D'E' spans from $x=0$ to $x=10$, so $D'E' = 10$.

Step2: Calculate scale factor

Scale factor is $\frac{\text{Length of image side}}{\text{Length of pre-image side}}$.
$\text{Scale factor} = \frac{D'E'}{DE} = \frac{10}{4}$

Step3: Simplify the fraction

Reduce $\frac{10}{4}$ by dividing numerator and denominator by 2: $\frac{10\div2}{4\div2} = \frac{5}{2}$

Answer:

$\frac{5}{2}$