The midpoint of line segment AB is (3, -1). Point A is at (2, 4). Where is point B located?
Let's use the midpoint formula to find the coordinates of point B. The midpoint formula is
midpoint = ( (x1 + x2)/2 , (y1 + y2)/2 )
Using this formula, we can solve for the x and y coordinates of point B.
The x-coordinate of the midpoint is 3.
The x-coordinate of point A is 2.
So, (2 + x-coordinate of B)/2 = 3
2 + x-coordinate of B = 6
x-coordinate of B = 6 - 2
x-coordinate of B = 4
The y-coordinate of the midpoint is -1.
The y-coordinate of point A is 4.
So, (4 + y-coordinate of B)/2 = -1
4 + y-coordinate of B = -2
y-coordinate of B = -2 - 4
y-coordinate of B = -6
Therefore, point B is located at coordinates (4, -6).
To find the location of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, (x, y), between two points (x1, y1) and (x2, y2) can be found by averaging their x-coordinates and averaging their y-coordinates.
In this case, we have the midpoint (3, -1) and point A (2, 4). Let's denote the coordinates of point B as (x2, y2). Now we can use the midpoint formula to set up the equations:
x = (x1 + x2) / 2 --> 3 = (2 + x2) / 2
y = (y1 + y2) / 2 --> -1 = (4 + y2) / 2
To find the x-coordinate of point B, we can rearrange the first equation and solve for x2:
3 = (2 + x2) / 2
6 = 2 + x2
4 = x2
So the x-coordinate for point B is 4.
Similarly, let's solve for the y-coordinate of point B:
-1 = (4 + y2) / 2
-2 = 4 + y2
-6 = y2
Therefore, the y-coordinate for point B is -6.
Putting it all together, the coordinates of point B are (4, -6).
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 with endpoints (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, we know that the midpoint is (3, -1) and point A is (2, 4). Let's substitute these values into the formula:
(x1 + x2) / 2 = 3
(y1 + y2) / 2 = -1
Substituting the coordinates of point A:
(2 + x2) / 2 = 3
(4 + y2) / 2 = -1
Now, we can solve for x2 and y2:
2 + x2 = 6
4 + y2 = -2
Solving for x2:
x2 = 6 - 2
x2 = 4
Solving for y2:
y2 = -2 - 4
y2 = -6
Therefore, point B is located at (4, -6).