[tex] d= \sqrt{ (x_2 - x_1)^2 + (y_2 - y_1)^2 }[/tex]
[tex]d^2= (x_2 - x_1)^2 + (y_2 - y_1)^2 }[/tex]
[tex]d^2 - (x_2 - x_1)^2 = (y_2 - y_1)^2 }[/tex]
[tex]|y_2 - y_1| = \sqrt{ d^2 - (x_2 - x_1)^2}[/tex]
Let's assume y₂ ≥ y₁. This is wrong; we shouldn't assume that; the question writers did this problem incorrectly. But we'll continue to get the answer they want you to choose.
[tex]y_2 - y_1 = \sqrt{ d^2 - (x_2 - x_1)^2}[/tex]
[tex]y_2 = y_1 + \sqrt{ d^2 - (x_2 - x_1)^2}[/tex]
Answer: A
The real answer is none-of-the-above. It's bad when the teachers who write these questions don't really know what they're doing.
The correct answer is y₂ is ambiguous:
[tex]y_2 = y_1 \pm \sqrt{ d^2 - (x_2 - x_1)^2}[/tex]
