Question

4) Find the length of the median BE of A ABC where A =
A = (10, 6),
B = (-2, 2) and C = (6, 10).​

Answer 1

Step-by-step explanation:

midpoint of AC

$( \frac{x1 + x2}{2} \frac{y1 + y2}{2}) = \\ ( \frac{10 + 6}{2} \frac{10 + 6}{2}) = (8 \: 8) \\ length \:of \: median =$

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ = \sqrt{ {( - 2 - 8)}^{2} + {(2 - 8)}^{2} } \\ = \sqrt{100 + 36} \\ = \sqrt{136} units$

Answer 2

Step-by-step explanation:

midpoint of AC

\begin{gathered}( \frac{x1 + x2}{2} \frac{y1 + y2}{2}) = \\ ( \frac{10 + 6}{2} \frac{10 + 6}{2}) = (8 \: 8) \\ length \:of \: median = \\ \ \end{gathered}

(

2

x1+x2

2

y1+y2

)=

(

2

10+6

2

10+6

)=(88)

lengthofmedian=

\begin{gathered} \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ = \sqrt{ {( - 2 - 8)}^{2} + {(2 - 8)}^{2} } \\ = \sqrt{100 + 36} \\ = \sqrt{136} units\end{gathered}

(x2−x1)

2

+(y2−y1)

2

=

(−2−8)

2

+(2−8)

2

=

100+36

=

136

units

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