Question

Plzz help me in the below question:-
*The coordinate of the vertices of a triangle are (-1,3), (-3,2) & (5,-1) respectively. Show that the length of the median through the vertex A is √41/4 units.
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Answer 1

Step-by-step explanation:

Given:Find the length of the median AP of ∆ABC whose vertices are A(–1, 3), B( –3,2) and C(5,-1).

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(-3,2)=> Let (x1,y1)

C(5,-1)=>Let (x2,y2)

Co-ordinate of P

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

Thus,

P(1,1/2)

Length of Median AP:

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

A(-1,3) and P(1,1/2)

$AP = \sqrt{( {-1 -1 )}^{2} +\big ( {3 - \frac{1}{2}\big)}^{2} }$

$AP= \sqrt{( {-2)}^{2} + \bigg( {\frac{5}{2}}\bigg)^{2} }$

$AP= \sqrt{4 + \frac{25}{4} }$

$AP=\sqrt{ \frac{16+25}{4} }$

$AP=\sqrt{ \frac{41}{4} }\:units$

Thus,

Length of Median AP is √(41/4)units.

Hence proved.

Hope it helps you.

To learn more on brainly:

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

https://brainly.in/question/29969964

Answer 2

Answer:

O bhai sahab yah Kaun Hai DP Mein Kiska naam hai

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