find the coordinates of g if f(1, 3.5) is the midpoint of gj and j has coordinates (6, -2)

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

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tutorconsortium005 tutorconsortium005 · Answer 2 · 2022-06-25T04:50:36-04:00

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) = ($\frac{(x1+x2)}{2}$, $\frac{(y1+y2)}{2}$)

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) = ($\frac{(6+x)}{2}$, $\frac{(-2+y)}{2}$)

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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