Let $L$ be the point $(t, t)$ in $x y$-plane and $M$ be a point on the $y$-axis such that $L M$ has slope $t$. Then the locus of the midpoint of $L M$ as $t$ varies over all real numbers is

• A

  $y=2 x^2-2 x$
• B

  $y=-2 x^2$
• Correct answer
  C

  $y=-2 x^2+2 x$
• D

  $y=2 x^2+2 x$

Hence, the correct answer is option: 'C'.