Given that,
The coordinates of A = (-10,-8)
The coordinates of B = (80,37)
To find,
The coordinates of a point that partitions segment AB in a ratio of 4:5.
Solution,
Let the coordinate of required point is (x,y). We can use section formula to find it as follows :
The section formula is :
[tex](x,y)=(\dfrac{m_2x_1+m_1x_2}{m_1+m_2},\dfrac{m_2y_1+m_1y_2}{m_1+m_2},)[/tex]
We have,
m₁ =4, m₂ = 5, x₁ = -10, x₂ = 80, y₁ = -8, y₂ = 37
Using all the values,
[tex](x,y)=(\dfrac{5(-10)+4(-10)}{4+5},\dfrac{5(-8)+4(37)}{4+5})\\\\=(-10,12)[/tex]
So, the required point in which AB is divided is (-10,12)
