the midpoint of line segment AB is (3,-1). point a is at (2,4). where is point b located?
(-2,5)
(4,-6)
(5/2,3/2)
(5,-4)
To find the location of point B, we need to use the midpoint formula.
Midpoint formula: (x, y) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Given: Midpoint (3, -1) and Point A (2, 4)
Using the midpoint formula, we can substitute the given values:
(x, y) = ((2 + x₂)/2, (4 + y₂)/2)
Simplifying the equation:
(3, -1) = ((2 + x₂)/2, (4 + y₂)/2)
Now equating the x-coordinates:
2 + x₂ = 2(3)
2 + x₂ = 6
x₂ = 6 - 2
x₂ = 4
Equating the y-coordinates:
4 + y₂ = 2(-1)
4 + y₂ = -2
y₂ = -2 - 4
y₂ = -6
Therefore, the location of point B is (4, -6).
The correct answer is:
(4, -6)