Respuesta :

Nayefx

Answer:

[tex] \rm\displaystyle D) \left (1,3\right)[/tex]

Step-by-step explanation:

well to figure out the point we can consider the following formula:

[tex] \rm\displaystyle \text C(x,y)= \left (\frac{m x_{2} + n x_{1} }{m + n} , \frac{m y_{2} + n y_{1} }{m + n} \right)[/tex]

from the given we acquire that,

  • [tex](x _{1}, y_{1}) = ( - 1,7)[/tex]
  • [tex](x _{2}, y_{2}) = ( 4, - 3)[/tex]
  • [tex]m : n = 2 : 3[/tex]

therefore substitute:

[tex] \rm\displaystyle \text C(x,y)= \left (\frac{(2) (4)+ 3( - 1) }{2 + 3} , \frac{(2) ( - 3) + (3)(7)}{2 + 3} \right)[/tex]

simplify multiplication:

[tex] \rm\displaystyle \text C(x,y)= \left (\frac{8 - 3 }{2 + 3} , \frac{ - 6+ 21}{2 + 3} \right)[/tex]

simplify:

[tex] \rm\displaystyle \text C(x,y)= \left (\frac{5}{5} , \frac{ 15}{5} \right)[/tex]

simplify division:

[tex] \rm\displaystyle \text C(x,y)= \left (1,3\right)[/tex]

hence our answer is D)

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MiReU

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

Points => (-1, 7) & (4, -3)

Ratio => 2 : 3

(x₁, y₁) = (-1, 7)

(x₂, y₂) = (4, -3)

(m₁, m₂) = (2, 3)

Formula = [tex]\large\left (\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}} \right)[/tex]

Points which divide the line segment

= [tex]( \frac{2 \times 4 + 3 \times - 1}{2 + 3}, \frac{2 \times -3 + 3 \times 7}{2 + 3})[/tex]

[tex] =( \frac{8 - 3}{5} , \frac{ - 6 + 21}{5}) \\ = ( \frac{5}{5} , \frac{15}{5} ) \\ = (1,3)[/tex]

Answer => (1, 3) [option D]

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