To find the length of side \( YZ \), we will use the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
The coordinates of points \( Y \) and \( Z \) are:
- \( Y (-4, 6) \)
- \( Z (-2, 2) \)
Now we can apply the distance formula to find \( YZ \):
\[ YZ = \sqrt{((-2) - (-4))^2 + (2 - 6)^2} \]
Calculating the differences:
\[ (-2) - (-4) = -2 + 4 = 2 \] \[ 2 - 6 = -4 \]
Substituting these values into the formula gives:
\[ YZ = \sqrt{(2)^2 + (-4)^2} \]
Calculating the squares:
\[ YZ = \sqrt{4 + 16} = \sqrt{20} \]
Simplifying \( \sqrt{20} \):
\[ \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} \]
Now, we can calculate numerical value for \( 2\sqrt{5} \):
Using \( \sqrt{5} \approx 2.236 \):
\[ 2\sqrt{5} \approx 2 \cdot 2.236 \approx 4.472 \]
Rounding to one decimal place:
\[ 4.472 \approx 4.5 \]
So, the length of side \( YZ \) is approximately \( \boxed{4.5} \).