# 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) $9$

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)

$9$

Exams
Articles
Questions