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The vertices of a triangle are A(-1,3), B(1,-1), C(5,1). Find the length of the median through the vertex C.

Posted by Arpit Singla 7 years, 3 months ago

CBSE > Class 10 > Mathematics

1 answers

Naveen Sharma 7 years, 3 months ago

Let the points A(-1, 3), B(1, -1) and C(5, 1) be the vertices of a triangle ABC.

We know median is the line segment joining the mid point of line to opposite vertex.

Let D be the mid point of AB. Then the coordinate of D

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1 +} y_{2}}{2}) (\frac{- 1 + 1}{2}, \frac{3 - 1}{2}) (0, 1)$

Coorditane of D( 0,1)

Lenght of Median CD=

Using distance formula

$\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \sqrt{{(5 - 0)}^{2} + (1 - 1)^{2}} \sqrt{25 + 0} \sqrt{25} 5$

1Thank You

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