1. The problem is to plot the point B with coordinates $\left(\frac{5}{2}, 3\right)$ on a Cartesian plane. 2. The coordinates $\left(\frac{5}{2}, 3\right)$ mean the point is located at $x=2.5$ and $y=3$. 3. To plot this point, start at the origin $(0,0)$. 4. Move $2.5$ units to the right along the x-axis. 5. From there, move $3$ units up along the y-axis. 6. Mark the point at this position. This completes the plotting of point B at $\left(2.5, 3\right)$.