Question

How to find the length of a median of a triangle with vertices?

Answer 1

How to find the length of a median of a triangle with vertices?

Answer 2

Step-by-step explanation:

*To show the method of finding length of one median,taking one example.

Let

Given:Find the length of the median AP of ∆ABC whose vertices are A(–1, 1), B(5, –3) and C(3, 5).

To find:

Length of median AP.

Solution:

Draw the triangle roughly,as shown in attachment.

Since P is midpoint of BC.

Find the co-ordinate of P:

$Mid - point \: P(x,y)= P\bigg( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\bigg )$

Thus,

B(5,-3)=> Let (x1,y1)

C(3,5)=>Let (x2,y2)

Co-ordinate of P

$x = \frac{5 + 3}{ 2} = \frac{8}{2} = 4 \\ \\ y = \frac{ - 3 + 5}{2} = \frac{2}{2} = 1$

Thus,

P(4,1)

Length of Median AP:

$\boxed{Distance \: formula = \sqrt{( {x_2 - x_1)}^{2} + ( {y_2 - y_1)}^{2} } }$

A(-1,1) and P(4,1)

$AP = \sqrt{( {4 + 1)}^{2} + ( {1 - 1)}^{2} } \\ \\ AP= \sqrt{( {5)}^{2} + ( {0)}^{2} } \\ \\ AP= 5 \: units$

Thus,

Length of Median AP is 5 units.

Hope it helps you.

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