3

Let $A, B, C, D$ and $E$ be five points marked in clockwise order, on the unit circle in the plane (with centre at origin). Let $\alpha$ and $\beta$ be real numbers and set $f(p)=\alpha x+\beta y$ where $P$ is a point whose coordinates are $(x,y)$. Assume that $f(A)=10, f(B)=5, f(C)=4$ and $f(D)=10$. Which of the following are impossible?

a) $f(E)=2$

b) $f(E)=4$

c) $f(E)=5$

user642796
  • 52,188
tattwamasi amrutam
  • 12,802
  • 5
  • 38
  • 73
  • 1
    Hint: The line $AD$ split the plane into two components and the point $E$ is lying on different side from the pair $B$ and $C$. Since $f$ is constant along the line $AD$.... – achille hui Jan 15 '14 at 14:14
  • @achillehui Like to say more on your comment? – Mick Jun 22 '14 at 18:29

0 Answers0