Question

In what ratio does the point (-4,y) divide the line segment joining the points A(-6,10) and B(3,-8) hence find y

Answer 1

Let the the point which divides line be P and its cordinates be $(x , y)$ and the ratio in which they are divided be

$m_1 \: and \: m_2$.

By section formula we know ,

For x coordinate,

$x = \dfrac{m_1 \times x_2 + m_2 \times x_1}{m1 + m2}$

$-4 = \dfrac{m1 \times 3 +( -6)\times x_1}{m1 + m2}$

On cross multipying ,

$-4m_1 - 4m_2 = 3 m_1 - 6 m_2$

$-4m_1 - 3m_1 = - 6 m_2 + 4 m_2$

$-4m_1 - 3m_1 = - 6 m_2 + 4 m_2$

$-7m_1 = - 2 m_2$

$\frac{m_1}{m_2} = \frac{\cancel{-}2}{\cancel{-}7}$

So,the ratio in which they are divided is 2: 7

To find y,

By section formula,

$y = \dfrac{m_1 \times y_2 + m_2 \times y_1}{m1 + m2}$

$y = \dfrac{2 \times (-8) + 7 \times 10}{7 +2}$

$y = \dfrac{-16 + 70}{9}$

$y = \dfrac{54}{9}$

y=6.