Question

Calculate the ratio in which the line joining the points (4,6) and (-5,-4) is divided by the line y=3.Also,find the co-ordinates of the point of intersection.

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Answer 1

$\bold{Answer:}$

The co-ordinates of every point on the line y=3 will be of the type (x,3).

Now, $\large\boxed{ y= \frac{m_1y_2+m_2y_1}{m_1+m_2} }$

[Taking:(x,3)=(x,y),(4,6)=(x1y1) and (-5,-4)=(x2,y2)]

$\large\boxed{3=\frac{m_1*-4+m_2*6}{m_1+m_2} }= \bold{7m_1=3m_2=\frac{m_1}{m_2} } = \large\boxed{\frac{3}{7} }$

$\bold{3m_1+3m_2=-4m_!+6m_2=7m_1=3m_2}= \large\boxed{\frac{m_1}{m_2}=\frac{3}{7} }$.

So , the required ratio is 3:6.

Now, $\large\boxed{x=\frac{m_1x_2+m_2x_1}{m_1+m_2} = x=\frac{3*-5+7*4}{3+7} }=\bold{\frac{13}{10} }$

So, the required point of intersection = $\large{\boxed{\mathfrak{\frac{13}{10},3. }}$

Answer 2

Answer:

See below..

Step-by-step explanation: