Multiple choice

If $A(-1, 3), B(1, -1)$ and $C(5, 1)$ are the vertices of a triangle ABC find the length of the median passing through the vertex A.

  1. $5$ units
  2. $6$ units
  3. $15$ units

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Midpoint of BC = ((1+5)/2, (-1+1)/2) = (3, 0). Median from A(-1, 3) to (3, 0) has length = sqrt((3 - -1)^2 + (0 - 3)^2) = sqrt(4^2 + (-3)^2) = sqrt(16+9) = 5.

AI explanation

Find the midpoint of the side BC by averaging the coordinates of B(1, -1) and C(5, 1). The midpoint D is ((1+5)/2, (-1+1)/2), which simplifies to D(3, 0). Use the distance formula to find the length of the median from A(-1, 3) to D(3, 0). The distance is the square root of ((3 - (-1)) squared + (0 - 3) squared), which equals the square root of (16 + 9). The square root of 25 is 5, so the median is 5 units.

Keep practicing — related questions