Answer: (1, 3)
Explanation:
To find the coordinates of point F, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are given by the average of their respective coordinates:
Midpoint coordinates: ( (x₁ + x₂)/2, (y₁ + y₂)/2 )
In this case, we are given the coordinates of point E as (-5,1) and the midpoint as (-2,2). Let's substitute these values into the formula to find the coordinates of point F:
For the x-coordinate:
(x₁ + x₂)/2 = -2
Substituting x₁ = -5:
(-5 + x₂)/2 = -2
Multiplying both sides by 2:
-5 + x₂ = -4
Adding 5 to both sides:
x₂ = 1
So, the x-coordinate of point F is 1.
For the y-coordinate:
(y₁ + y₂)/2 = 2
Substituting y₁ = 1:
(1 + y₂)/2 = 2
Multiplying both sides by 2:
1 + y₂ = 4
Subtracting 1 from both sides:
y₂ = 3
Therefore, the coordinates of point F are (1, 3).