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)
Learn more about finding mid-point here:
https://brainly.com/question/13115533
#SPJ2
