Math, asked by madasnaresh6, 14 hours ago

3) If A (3,2), B (-4,-4) & C (5-8) are the verticles of a triangle then the length of median through Vertex c is A ) 85 B) 65 c) None of these d) 75​

Answers

Answered by user0888
57

\rm\large\underline{\text{Main idea}}

It is given that,

\rm\cdots\longrightarrow C(5,-8)

The median of \rm A(3,2) and \rm B(-4,-4) is,

\rm\cdots\longrightarrow M(-\dfrac{1}{2},-1)

Provided that the median \rm M goes through \rm C.

\rm\large\underline{\text{Solution}}

By distance formula,

\rm\cdots\longrightarrow\overline{CM}=\sqrt{(5+\dfrac{1}{2})^2+(-8+1)^2}

\rm\cdots\longrightarrow\overline{CM}=\sqrt{\dfrac{121}{4}+49}

\rm\cdots\longrightarrow\overline{CM}=\sqrt{\dfrac{121+196}{4}}

\rm\cdots\longrightarrow\overline{CM}=\dfrac{\sqrt{317}}{2}

Choice c, none of the above is the answer.

\rm\large\underline{\text{Extra! Information}}

\boxed{\textrm{Midpoint formula}}

The midpoint \rm M is,

\rm\cdots\longrightarrow M(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2})

\boxed{\textrm{Internal section formula}}

When a point \rm P internally divides in a ratio of \rm m:n,

\rm\cdots\longrightarrow P(\dfrac{mx_{2}+nx_{1}}{m+n},\dfrac{my_{2}+ny_{1}}{m+n})

\boxed{\textrm{External section formula}}

When a point \rm P externally divides in a ratio of \rm m:n(m>n),

\rm\cdots\longrightarrow P(\dfrac{mx_{2}-nx_{1}}{m-n},\dfrac{my_{2}-ny_{1}}{m-n})

Provided that two points are \rm (x_{1},y_{1}) and \rm (x_{2},y_{2}).

Answered by singhsuryanshu341
54

Step-by-step explanation:

given :

  • A (3,2), B (-4,-4) & C (5-8) are the verticles of a triangle

to find :

  • the length of median through Vertex C = ?

Solution :

  • vertices of traingle ABC

  • A (3,2), B (-4,-4) & C (5-8)

  • traingle ABC = √ (5+ 1/2 + ( -8 +1)

  • traingle ABC = √121/4 + 49

  • traingle ABC = √ 121+ 196/4

  • traingle ABC = √317/2

hence, option C is correct none

of these

learn more :

formula of Distance :

distance =√(x2 - X1) + (y2 - y1)

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