The midpoint of line segment AB is (3.5, 1). Point A is at (2, 6). Where is point B located?
To find the location of point B, we need to use the formula for the midpoint of a line segment.
The formula for the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Given that the midpoint is (3.5, 1) and point A is at (2, 6), we can substitute these values into the formula and solve for point B.
((2 + x₂)/2, (6 + y₂)/2) = (3.5, 1)
Simplifying the equation, we get:
(2 + x₂)/2 = 3.5
6 + y₂)/2 = 1
Now we can solve for x₂ and y₂:
2 + x₂ = 3.5 * 2
6 + y₂ = 1 * 2
2 + x₂ = 7
6 + y₂ = 2
Subtracting 2 from both sides of the first equation, we get:
x₂ = 5
Subtracting 6 from both sides of the second equation, we get:
y₂ = -4
Therefore, point B is located at (5, -4).