Question

find the coordinates of the points of trisection of the line segment joining the points A(2,-2)and B(-7,4) by step by step

Answer 1

Refer to the attached image.

We have to find the coordinates of the points of trisection of the line segment joining the points A(2,-2)and B(-7,4).

Case 1: Assume that the coordinate P divides the line segment AB in the ratio 1:2

By applying cross section formula, which states:

" When a line segment joining coordinates $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is divided by some coordinate in the ratio $m_{1}:m_{2}$, then the coordinates are given by the formula:

$(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}} , \frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}})$

Substituting the values in the above formula,

We get coordinate P = $(\frac{1(-7)+2(2)}{1+2} , \frac{1(4)+2(-2)}{1+2})$

P = (-1, 0)

Case 2:

Assume that the coordinate Q divides the line segment AB in the ratio 2:1

By applying cross section formula, which states:

" When a line segment joining coordinates $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is divided by some coordinate in the ratio $m_{1}:m_{2}$, then the coordinates are given by the formula:

$(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}} , \frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}})$

Substituting the values in the above formula,

We get coordinate Q = $(\frac{2(-7)+1(2)}{2+1} , \frac{2(4)+1(-2)}{2+1})$

Q = (-4, 2)

So, the coordinates are P(-1,0) and Q(-4,2).