Three vertices of a parallelogram ABCD are A(-2,3) B(7,12) C(11,-5). Find the length of the diagonal BD

Well, have those points plotted on a graph.

AB is parallel to CD (gradient AB = gradient CD)
BC is parallel to AD (gradient BC = gradient AD)

On your graph, draw a line from C parallel to AB, another line from A parallel to BC. Where both lines meet is the point D.

You may go through equations, and solving them simultaneously. Find gradient BC and AB. Use equation formula to find equation AD and BD. Solve both equations to get D.

Then, use distance formula to find the distance BD.