Stuart Kovinsky wrote:
Almost certainly this would be a great question to backsolve (i.e. work backwards from the answers, eyeballing the diagram). In future, please post the choices!
I'm curious how it would be helpful here to have answer choices like:
A) sqroot(2)
B) sqroot(3)
C) 4 - 2*sqroot(2)
D) 2
E) sqroot(10)
Backsolving does not seem straightforward, at least not to me.
We have two endpoints of a diagonal of a square. We can use the following:
-the midpoint of one diagonal is the midpoint of the other diagonal;
-the diagonals are perpendicular.
If (0,6) and (6,2) are endpoints, (3,4) is the midpoint.
From (0,6) to (3,4), we go right 3 and down 2; that is, we increase x by 3 and decrease y by 2: the slope is -2/3. Consider the perpendicular diagonal- its slope is the negative reciprocal, i.e. 3/2. From (3,4), on a perpendicular line, to find a point the same distance from (3,4) as (0,6) is, we can decrease x by 2 and decrease y by 3, or we can increase x by 2 and increase y by 3. The endpoints of the other diagonal are (1,1) and (5,7).
The distance from (0,0) to (1,1) is sqrt(2).
