Respuesta :

alyssabrown73

Answer:

(-2,5)

Step-by-step explanation:

DᴀʀᴋPᴀʀᴀᴅᴏx

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We know that mid - point of a line segment divides it into two equal parts, that is it divides the segment in the ratio of 1 : 1, so let's find the coordinates of the mid point of line segment joining points (-9 , 3) and (5 , 7).

let the coordinates of the points be x and y, now

  • [tex]m = 1[/tex]

  • [tex]n = 1[/tex]

  • [tex]x_2 = 5[/tex]

  • [tex]x_1 = - 9[/tex]

  • [tex]y_2 = 7[/tex]

  • [tex]y_1 = 3[/tex]

Using section formula :

value of x :

  • [tex]x = \dfrac{mx_2 - nx_1}{m + n} [/tex]

  • [tex]x = \dfrac{(1 \times 5) - (1 \times - 9)}{1 + 1} [/tex]

  • [tex]x = \dfrac{5 - ( - 9)}{2} [/tex]

  • [tex]x = \dfrac{5 + 9}{2} [/tex]

  • [tex]x = \dfrac{14}{2} [/tex]

  • [tex]x = 7[/tex]

value of y :

  • [tex]y = \dfrac{my_2 -ny_1 }{m+ n} [/tex]

  • [tex]y = \dfrac{(1 \times 7) - (1 \times 3)}{1 + 1} [/tex]

  • [tex]y = \dfrac{7 - 3}{2}[/tex]

  • [tex]y = \dfrac{4}{2} [/tex]

  • [tex]y = 2[/tex]

So, coordinates of the point which is midpoint of the given line is :

[tex] \boxed{ \boxed{ (7, 2)}}[/tex]

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