Question

Two vertices of a right isosceles triangle are (1,1) and (2,0). Which of the following could be the coordinates of the third vertex of this triangle?

Answer 1

This is like Theorem of pythagoras. Finding the slant

Answer 2

Finding the slant AC is the hypothenuse, by \[\frac{ 0-1 }{ 2-1 }= \frac{ -1 }{ 1 }=-1\]

Answer 3

Given that it is an isosceles triangle, it means that sides AB and BC have the same length or slant. Let the coordinates of B be (x,y)
in an equation we can make \[\frac{ 1-y }{ 1-x }=\frac{ 0-y }{ 2-x }\]

Answer 4

Oops, guess I am wrong. Never mind with my work.