Multiple choice

$\hat { AB } =-3{ \hat { i } }+4{ \hat { k } }$ and $\hat { BC } =-\overline { i } -2\overline { k } $ are the sides of the triangle $ ABC$ then the length of the median $AM$ is

  1. $\sqrt{\dfrac{25}{2}}$
  2. $\sqrt{\dfrac{45}{2}}$
  3. $\displaystyle \dfrac{\sqrt{65}}{2}$
  4. $\displaystyle \dfrac{\sqrt{85}}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

AB = -3i + 4k, BC = -i - 2k. AC = AB + BC = -4i + 2k. Median AM connects A to midpoint M of BC. M = (B+C)/2. AM = (AB + AC)/2 = ((-3i + 4k) + (-4i + 2k))/2 = (-7i + 6k)/2. Length = sqrt((-7/2)^2 + (6/2)^2) = sqrt(49/4 + 36/4) = sqrt(85/4) = sqrt(85)/2.

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