When we subsitute the given distance and the given coordinates for points A and B into the distance formula, we get the following equation.
sqrt[(x2 - x1)^2 + (y2 - y1)^2] = 0
We can clean this up a bit, by squaring both sides.
(x2 - x1)^2 + (y2 - y1)^2 = 0
Now, consider the following statements and questions.
(1) The expression x2 - x1 represents some number.
(2) The expression y2 - y1 represents some number.
(3) The sum of the squares of these two numbers is zero.
(4) What do the values of the two expressions x2 - x1 and y2 - y1 actually need to be, in order for the sum of their squares to equal zero?
(5) Once you answer question (4), consider the following two questions.
(6) Now that you know the actual value of the expression x2 - x1, what can you say about the relationship between the number x1 and the number x2?
(7) Now that you know the actual value of the expression y2 - y1, what can you say about the relationship between the number y1 and the number y2?
(8) By stating the relationships asked for in (6) and (7), you will have explained why the coordinates of points A and B must be the same.
If I wrote anything that you do not understand, OR, if you cannot answer any of the questions above, then please say so, and somebody will help you further.
