Question

Find the coordinates

of the points of trisection

(i.e., points dividing the

line segment, in three

equal parts) of the line

segment joining the

points (2, -2) and

(-7, 4). ​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Points are (2,-2) and (-7,4)}$

$\underline{\textsf{To find:}}$

$\textsf{Points of trisection of line segment joining}$

$\textsf{given points}$

$\underline{\textsf{Solution:}}$

$\textsf{Let the given points be A(2,-2) and B(-7,4)}$

$\textsf{Let P and Q be the points of trisection}$

$\textsf{Then P and Q divides AB internally in the ratio 1:2 and 2:1 respectively}$

$\textsf{By Section formula, the coordinates of P is}$

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

$\mathsf{(\dfrac{1(-7)+2(2)}{1+2},\dfrac{1(4)+2(-2)}{1+2})}$

$\mathsf{(\dfrac{-7+4}{3},\dfrac{4-4}{3})}$

$\mathsf{(\dfrac{-3}{3},\dfrac{0}{3})}$

$\mathsf{(-1,0)}$

$\textsf{Also, the coordinates of Q is}$

$\mathsf{(\dfrac{2(-7)+1(2)}{2+1},\dfrac{2(4)+1(-2)}{2+1})}$

$\mathsf{(\dfrac{-14+2}{3},\dfrac{8-2}{3})}$

$\mathsf{(\dfrac{-12}{3},\dfrac{6}{3})}$

$\mathsf{(-4,2)}$

$\underline{\textsf{Answer:}}$

$\textsf{The points of trisection are (-3,0) and (-4,2)}$

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