Question

AD is a median of ΔABC with vertices A (5, -6), B (6, 4) and C (0, 0). Length AD is equal to ______.

Options

• `sqrt68` units

• `2sqrt15` units

• `sqrt101` units

• 10 units

Answer 1

AD is a median of ΔABC with vertices A (5, -6), B (6, 4) and C (0, 0). Length AD is equal to `underlinebb(sqrt68  "units")`.

Explanation:

Coordinates of D(x, y).

Using the mid-point formula, the coordinates of the midpoint of BC are 

Co-ordinates of D(x, y) = `((6 + 0)/2, (4 + 0)/2)`

= (3, 2)

Now, length of AD = `sqrt((x_4-x_1)^2+(y_4-y_1)^2)`

= `sqrt((3 - 5)^2 + (2 + 6)^2)`

= `sqrt(4 + 64)`

= `sqrt68` units