PowerShell can place the mouse cursor anywhere on your screen. Here's the code:
[system.Reflection.Assembly]::LoadWithPartialName("Microsoft.Forms") | Out-Null
[System.Windows.Forms.Cursor]::Position = New-Object System.Drawing.Point(500,100)
[System.Windows.Forms.Cursor]::Position = New-Object System.Drawing.Point(500,100)
This would have placed the cursor at x=500 and y=100.