AD is a median of ABC with vertices A(5, –6), B(6, 4) and C(O, O). Length AD is equal to :

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Solution

Q.
AD is a median of $∆$ ABC with vertices A(5, –6), B(6, 4) and C(O, O). Length AD is equal to :

1 $\sqrt{68}$ units

2 $2 \sqrt{15}$ units

3 $\sqrt{101}$ units

4 10 units

Ans.
(1)

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

Co-ordinates of $D (x, y) = (\frac{6 + 0}{2}, \frac{4 + 0}{2}) = (3, 2)$

Now, length of $A D = \sqrt{{(5 - 3)}^{2} + {(- 6 - 2)}^{2}} = \sqrt{4 + 64} = \sqrt{68}$

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