Question

Find the coordinates of the points of trisection of the line segment joining the points A(–5, 6) and B(4, 3)

Answer 1

Answer:

The points of trisection are (-2,5) and (1,4)

Step-by-step explanation:

Find the coordinates of the points of trisection of the line segment joining the points A(–5, 6) and B(4, 3)

Formula used:

$\text{The co ordinates of thepoint which divides the line segment joining}\:(x_1,y_1)\:\text{and}\:\\(x_2,y_2)\:\text{internally in the ratio m:n is}$

$\boxed{(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})}$

Given points are A(–5, 6) and B(4, 3)

Let P and Q be the points of trisection of line segment AB

Clearly, P divides AB internally in the ratio 1:2

Then P is

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$\implies\:P\:is\:(\frac{1(4)+2(-5)}{1+2},\frac{1(3)+2(6)}{1+2})$

$\implies\:P\:is\:(\frac{-6}{3},\frac{15}{3})$

$\implies\:P\:is\:(-2,5)$

Clearly, Q divides AB internally in the ratio 2:1

Then Q is

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

$\implies\:Q\:is\:(\frac{2(4)+1(-5)}{2+1},\frac{2(3)+1(6)}{2+1})$

$\implies\:Q\:is\:(\frac{3}{3},\frac{12}{3})$

$\implies\:Q\:is\:(1,4)$