In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x =4. Then area of ABC (in sq. units)

  • Option 1)

    12

  • Option 2)

    4

  • Option 3)

    5

  • Option 4)

    9

 

Answers (1)
H Himanshu

As we learned

 

Selection formula -

x= \frac{mx_{2}+nx_{1}}{m+n}

y= \frac{my_{2}+ny_{1}}{m+n}

- wherein

If P(x,y) divides the line joining A(x1,y1) and B(x2,y2) in ration m:n

 

 

 

Mid-point formula -

x= \frac{x_{1}+x_{2}}{2}

y= \frac{y_{1}+y_{2}}{2}

 

- wherein

If the point P(x,y) is the mid point of line joining A(x1,y1) and B(x2,y2) .

 

 

Median through C is x=4

So coordinates of C are (4,y)

mid point of A(1,2) and C(2y) is \left ( \frac{5}{2},\frac{2+y}{2} \right )

Centroid C1 = (y,1)  passes through medians  x=1 and x+y=4

\bigtriangleup ABC=3\bigtriangleup AC_{1}C=3\times \frac{1}{2}\times 3\times 2=9

 

 


Option 1)

12

Option 2)

4

Option 3)

5

Option 4)

9

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