Given:
Endpoints of a line segment EF are E(-3,8) and F(7,-7).
Point P divides the segment EF such that EP:PF = 2:3.
To find:
The coordinates of the point P.
Solution:
Section formula: If a point divides a line segment in m:n, then the coordinates of the points are:
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
It is given that EP:PF = 2:3. It means the point P divides the segment EF in 2:3.
Using section formula, we get
[tex]P=\left(\dfrac{2(7)+3(-3)}{2+3},\dfrac{2(-7)+3(8)}{2+3}\right)[/tex]
[tex]P=\left(\dfrac{14-9}{5},\dfrac{-14+24}{5}\right)[/tex]
[tex]P=\left(\dfrac{5}{5},\dfrac{10}{5}\right)[/tex]
[tex]P=\left(1,2\right)[/tex]
Therefore, the coordinates of the point P are (1,2).
