Question

find the coordinates of the points of trisection of the line segment joining - 4,7 and 2,1​

Answer 1

Answer:

P(-2,8/3) & Q(0,3)

Step-by-step explanation:

Pls refer below.......

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Answer 2

Answer:

Let (4,7) be A ; (2,1) be B ; the points of trisection be C and D

A_______C_______D_______B

AC : CD : BD = 1 : 1 : 1

AC : BC = 1 : 2

BD : AD = 1 : 2

$C(x,y) = [\frac{mx_{1}+Mx_{2}}{m +M}, \frac{my_{1}+My_{2}}{m +M} ]$

$C(x,y) = [\frac{(1)(4)+(2)(2)}{1 +2}, \frac{(1)(7)+(2)(1)}{1 + 2}]$

$C(\frac{8}{3} , 3)$ ... (I)

$D(x,y) = [\frac{mx_{1}+Mx_{2}}{m +M}, \frac{my_{1}+My_{2}}{m +M} ]$

$D(x,y) = [\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}]$

$D(x,y) = [\frac{\frac{8}{3} +2}{2}, \frac{3+1}{2}]$

$D(\frac{7}{3} ,2)$ ... (II)

Therefore, C and D are the points trisecting AB

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