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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.

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15 units

None of these

6 units

5 units

answer is A.

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Detailed Solution

Given that, A(-1, 3), B(1, -1) and C(5, 1) are the vertices of a triangle ABC.
We need to find the length of the median through A.
Let AD be the median through A.
Midpoint of two point

{(x}_{1}, y_{1})

{(x}_{2}, y_{2})

is ,

(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

.
Since, AD is the median, D is the midpoint of BC,
Therefore, coordinates of D are,

\Rightarrow (\frac{1 + 5}{2}, \frac{- 1 + 1}{2}) = (3, 0)

Now, the distance between the points

{(x}_{1}, y_{1})

{(x}_{2}, y_{2})

is given by the formula,
Distance =

\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} + y_{1})}^{2}}

Length of median AD by distance formula,

AD = \sqrt{{(3 + 1)}^{2} {+ (0 - 3)}^{2}}

\Rightarrow AD = \sqrt{{(4)}^{2} {+ (- 3)}^{2}}

\Rightarrow AD = \sqrt{16 + 9}

\Rightarrow AD = \sqrt{25}

\Rightarrow AD = 5

Thus, the length of the median passing through A is 5 units.
Therefore, option (1) is correct.

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