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 midpoint formula.
The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
In this case, we know that the midpoint (M) is (3.5, 1) and one endpoint (A) is (2, 6).
Using the midpoint formula, we can set up the following equations:
3.5 = (2 + x₂)/2 and 1 = (6 + y₂)/2
Now let's solve these equations to find the coordinates of point B.
3.5 = (2 + x₂)/2
Multiply both sides by 2:
7 = 2 + x₂
Subtract 2 from both sides:
x₂ = 5
1 = (6 + y₂)/2
Multiply both sides by 2:
2 = 6 + y₂
Subtract 6 from both sides:
y₂ = -4
Therefore, point B is located at (5, -4).