The midpoint of line segment AB is (3, -1). Point A is at (2, 4). Where is point B located?
Responses
(4, -6)
(4, -6)
(5, -4)
(5, -4)
(-2, 5)
(-2, 5)
(52,32)
None of the provided responses are correct.
To find the location of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Given that the midpoint is (3, -1) and point A is (2, 4), we can set up the following equations:
(2 + x-coordinate of B) / 2 = 3
(4 + y-coordinate of B) / 2 = -1
Solving the first equation:
2 + x-coordinate of B = 6
x-coordinate of B = 6 - 2
x-coordinate of B = 4
Solving the second equation:
4 + y-coordinate of B = -2
y-coordinate of B = -2 - 4
y-coordinate of B = -6
Therefore, point B is located at (4, -6).
To find the location of point B, we can use the formula for the midpoint of a line segment. The midpoint formula is:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Given that the midpoint of line segment AB is (3, -1) and that point A is at (2, 4), we can substitute these values into the midpoint formula and solve for point B.
Let's denote the coordinates of point B as (x, y).
Using the midpoint formula:
3 = (2 + x)/2
-1 = (4 + y)/2
To solve for point B, we need to eliminate fractions by multiplying both sides of each equation by 2:
6 = 2 + x
-2 = 4 + y
Simplifying each equation, we get:
4 = x
-6 = y
Therefore, the coordinates of point B are (4, -6).
The correct response is:
(4, -6)