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Length of the median from B on AC where A (-1, 3), B (1, -1), C (5, 1) is:

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\sqrt{18}

units

\sqrt{10}

units

2 \sqrt{3}

units

4 units

answer is B.

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Detailed Solution

[1]
Given that, A (-1, 3), B (1, -1), C (5, 1).
We need to find the length of the median from B.
Let BE be the median from B on AC.
Then E is the midpoint of AC.
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})

Coordinates of E are

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

i.e. (2, 2),
Question Image

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}}

\Rightarrow BE = \sqrt{{(2 - 1)}^{2} + {(2 + 1)}^{2}}

\Rightarrow BE = \sqrt{1^{2} + 3^{2}}

\Rightarrow BE = \sqrt{10}

Thus, the length of median from B on AC is

\sqrt{10}

units.
Therefore, option (2) is correct.

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Length of the median from B on AC where A (-1, 3), B (1, -1), C (5, 1) is:

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