Question

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Answer 1

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:

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

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

$P=\left(\dfrac{2(7)+3(-3)}{2+3},\dfrac{2(-7)+3(8)}{2+3}\right)$

$P=\left(\dfrac{14-9}{5},\dfrac{-14+24}{5}\right)$

$P=\left(\dfrac{5}{5},\dfrac{10}{5}\right)$

$P=\left(1,2\right)$

Therefore, the coordinates of the point P are (1,2).