Answer :

publius
the midpoint of a line is equal to [tex] (x_{2}+ x_{1})/2[/tex] and [tex] (y_{2}+ y_{1})/2 [/tex]
[tex]1= (6+ x_{1})/2[/tex]                      [tex]3.5=(-2+ y_{1})/2 [/tex]
[tex]1*2=6+ x_{1} [/tex]                        [tex]3.5*2=-2+ y_{1} [/tex]
[tex]2-6= x_{1} [/tex]                            [tex]7+2= y_{1} [/tex]
[tex]-4= x_{1} [/tex]                              [tex]9= y_{1} [/tex]
   and thus pont g is at (-4,9)
 

The coordinates of g are (-4, 9). Since it is given that f(1, 3.5) is the midpoint of gj, these coordinates must lie in between the coordinates of g and j.

How to calculate mid-point when two coordinates are given?

Consider two coordinates as (x1, y1) and (x2, y2)

So, the mid-point is in between those two coordinates. That means it is of the same distance from both coordinates.

∴ mid-point coordinates (x, y) = ([tex]\frac{(x1+x2)}{2}[/tex], [tex]\frac{(y1+y2)}{2}[/tex])

Calculation:

The given mid-point is f(1, 3.5)

It is given that coordinates of j(6, -2)

The mid-point lies in between g and j

consider the coordinates of g as (x, y)

So,

(1, 3.5) = ([tex]\frac{(6+x)}{2}[/tex], [tex]\frac{(-2+y)}{2}[/tex])

On equating,

1 = (6 + x)/2

⇒ 2 = 6 + x

⇒ x = 2 - 6

∴ x = -4

and

3.5 = (-2 + y)/2

⇒ 3.5 × 2 = -2 + y

⇒ 7 = -2 + y

⇒ y = 7 + 2

∴ y = 9

So, the coordinates of g is ( -4, 9)

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