Question

If (1, 1), (5, 3) and (9, 2) are the vertices of a triangle, then the sum of lengths of medians of the triangle is

Answer 1

Answer:

Step-by-step explanation:

Median intersects the opposite side into 2 equal halves.

Coordinates of the base: A(1,1) & B(9,2)

So, the point at which the median intersects the base:

\frac{x_{2}+ x_{1}  }{2} = $\frac{9+1}{2} = \frac{10}{2} = 5$  

Hence our x coordinate is 5.

Y coordinate:

$\frac{y_{2}+ y_{1} }{2} = \frac{1+2}{2} = \frac{3}{2} = 1.5$

Our y coordinate is 1.5.

Let the point be D(5,1.5)

On applying distance formula for CD, we get CD = 1.5 units

This is our first median.

Similarly after calculating coordinates for sides BC and AC and applying distance formula, we get the medians as 6.18 and 6.

So, adding all 3,   1.5+6.18+6 , we get 13.68 units

Hope that helps you...

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