Question

1. There are infinite black and white dots on a plane. Prove that the distance between one black dot and one white dot is one unit.​

Answer 1

Explanation:

The statement is in general false: for example, if the black dots are all and only on the locus x=0x=0, while the white ones are all and only on the locus x=2x=2, then the assertion is false (we are using the Euclidean distance).

Probably there are some more hypothesis in the background OR the aim of the question is just to analyze the way the candidate faces a given mathematical problem, reaching conclusions which can be in contrast with the thesis of any given question.

Answer 2

refer to the attachment for the answer

$<svg height="210" width="500">\ \textless \ br /\ \textgreater \ <polygon points="100,10 40,198 190,78 10,78 160,198"\ \textless \ br /\ \textgreater \ style="fill:lime;stroke:black;stroke-width:5;fill-rule:nonzero;" />\ \textless \ br /\ \textgreater \ </svg>$