Question

The co-ordinates of the point P dividing the line segment joining the points A(3,3) and B (6,6) internally in the ratio 2:1 are​

Answer 1

Please refer to the attachment

Question

The co-ordinates of the point P dividing the line segment joining the points A(3,3) and B (6,6) internally in the ratio 2:1 are ___ .

$\bullet\sf \:Answer$

The required coordinates of P = (5,5)

Solution

We know that in order to find the co-ordinates of P we have to apply Section Formula .

Let the co-ordinates of P be ( x , y )

Then , according to Section Formula

$\boxed{ \sf (x , y) = (\dfrac{m_1 x_2 + m_2x_1}{m_1 + m_2} \: , \: \dfrac{m_1y_2 + m_2y_1}{m_1 + m_2})}$

Here in the above formula

On Implementing the above values in section formula we'll get

$\sf(x,y) = ( \frac{2 \times 6 + 1 \times 3}{2 + 1} \ ,\: \frac{2 \times 6 + 1 \times 3}{2 + 1} )$

$\boxed{ \sf(x,y) = ( \frac{12+ 3}{3} \ ,\: \frac{12+ 3}{3} )}$

${ \sf(x,y) = ( \frac{15}{3} ,\frac{15}{3} )} = \bf(5,5)$

So , I must conclude that abscissa as well as ordinate of point P is 5

Thankyou