Question 404397: Let a and b be real numbers. A line passes through points (a,b) and (b,a). Consider another three points (a+1,b-1), (b+1,a-1), ((a+b)/2,(a+b)/2). Which of the following is true regardless of the choice of a and b?
choose the answer and explain the reason to choose your response
Exactly two of the points lie on the line
All three of the points lie on the line
Exactly one of the points lies on the line
None of the points lie on the line
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! All three of the points lie on the same line.
The line through (a,b) and (b,a)has slope -1.
The line through(a,b) and (a+1,b-1) has slope -1.
The line through(a,b) and (b+1,a-1) has slope -1.
The point ((a+b)/2,(a+b)/2) is the midpoint of the points (a,b) and (b,a).
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