To find the length of the vertical side based on the given coordinates \((15, -3)\), \((19, -6)\), and \((15, -10)\), we will focus on the vertical coordinates (the second value in each pair).
We have two points with the same x-coordinate, which are \((15, -3)\) and \((15, -10)\). The length of the vertical side can be determined by finding the difference in the y-coordinates of these two points.
The y-coordinates are:
- For \((15, -3)\), the y-coordinate is \(-3\).
- For \((15, -10)\), the y-coordinate is \(-10\).
Now, we calculate the length:
\[ \text{Length} = |y_2 - y_1| = |-10 - (-3)| = |-10 + 3| = |-10 + 3| = |-7| = 7 \]
Thus, the length of the vertical side is 7 centimeters.