The answer is A
A line is the locus of points that: are the same distance from two points.
Let's prove this. Let's call the points (a,b) and (c,d) and equate the squared distance to (x,y)
[tex](x-a)^2+(y-b)^2 = (x-c)^2 + (y-d)^2[/tex]
[tex]x^2 - 2ax + a^2 + y^2 - 2by + b^2 = x^2 - 2cx + c^2 + y^2 - 2dx + d^2[/tex]
[tex]2(c-a)x + 2(d-b)y = c^2+d^2-a^2-b^2[/tex]
That's the equation for a line.
