Think of a situation when someone would need to make a measurement with extreme precision. Describe the setting, why the measurement must be so precise, and some of the consequences that might occur if it were not precise.

Ok, suppose you want to create a battery that fits exactly in the hole that is already created for an electric device, like a cellphone for example.

If the battery is slightly bigger, it will not enter the socket, and the battery will be a loss in time and resources.

If the battery is slightly smaller, it will move when it is in the socket, so the cell phone will shut down randomly when you move it, then this battery is also a loss in time and resources.

So you need to measure exactly the socket in order to make a battery that fits exactly inside of it with very good precision.  

This example can be extended for any electronic piece that you need to fit in a given space (for example in microtechnology, the precision of the measures is must be extreme because working with those things is really expensive and you can not mess up with the dimensions of the pieces)

Coplanar points are three or more points which lie in the same plane .A plane is a flat surface which extends without end in all directions. A set of points, lines, line segments, rays or any other geometrical shapes that lie on the same plane are said to be Coplanar.In the above figure given :Among all the options given a)C, H, E    b)B, K, H        c). A, B, K  are not lying in the same plane .

Points A, E, D are lying in the same plane and hence are coplanar.

Option D is the right answer.