Question

1 point
Point P which internally
divides the points A(-2, 1)
and B(1, 4) in the ratio 2:1
is *​

Answer 1

Answer:

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Answer 2

$\huge{\mathcal{\underline{\pink{Solution:-}}}}$

The point P(x , y) which divides the joining of points (x₁ , y₁) and (x₂ , y₂) in the ratio m : n internally is given by ,

$\large\rm\bold{\boxed{(x,y)\:=\:(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})}}$

Given points are A(-2 , 1 ) , B( 1 , 4 ) and ratio is 2 : 1

Let the Point be P( x , y )

By comparing we get ,

• x₁ = -2 , x₂ = 1
• y₁ = 1 , y₂ = 4
• m = 2 , n = 1

By applying section formulae ,

$\large\rm{\rightarrow{(x,y)\:=\:(\frac{2(1)+1(-2)}{2+1},\frac{2(4)+1(1)}{2+1})}}$

$\large\rm{\rightarrow{(x,y)\:=\:(\frac{0}{3},\frac{9}{3})}}$

$\large\rm{\rightarrow{(x,y)\:=\:(0,3)}}$

∴ The required point is (0,3)