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)
(5/2,3/2)
To find the location of point B, we need to consider the coordinates of point A and the midpoint of the line segment AB.
The x-coordinate of the midpoint is given as 3, and we know that it is the average of the x-coordinates of points A and B. Therefore, the x-coordinate of point B is 2 times the x-coordinate of the midpoint minus the x-coordinate of point A, which is:
2 * 3 - 2 = 6 - 2 = 4
Similarly, the y-coordinate of the midpoint is given as -1, and we know that it is the average of the y-coordinates of points A and B. Therefore, the y-coordinate of point B is 2 times the y-coordinate of the midpoint minus the y-coordinate of point A, which is:
2 * (-1) - 4 = -2 - 4 = -6
Therefore, point B is located at (4, -6).
The correct response is:
(4, -6)
To find the coordinates of point B, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment, given the coordinates of its endpoints, can be found by taking the average of the x-coordinates and the average of the y-coordinates.
Let's denote the coordinates of point B as (x, y). The coordinates of the midpoint of line segment AB are (3, -1), and the coordinates of point A are (2, 4).
Using the midpoint formula, we can set up the following equations:
(x + 2) / 2 = 3 (average of x-coordinates)
(y + 4) / 2 = -1 (average of y-coordinates)
To solve the equations, we can multiply both sides of the first equation by 2, and both sides of the second equation by 2:
x + 2 = 6
y + 4 = -2
Subtracting 2 from both sides of the first equation, we have:
x = 4
Subtracting 4 from both sides of the second equation, we have:
y = -6
Therefore, the coordinates of point B are (4, -6).
So, the correct answer is:
(4, -6)
To find the location of point B, we can use the formula for the midpoint of a line segment, which states that the coordinates of the midpoint are the average of the coordinates of the two endpoints.
Given that the midpoint of line segment AB is (3, -1) and point A is at (2, 4), we can apply the formula:
Midpoint coordinates = ((x1 + x2)/2, (y1 + y2)/2)
Substituting the known values into the formula:
(3, -1) = ((2 + x2)/2, (4 + y2)/2)
Now we can solve for the unknown values. Using the first coordinate:
3 = (2 + x2)/2
Multiply both sides of the equation by 2:
6 = 2 + x2
Subtract 2 from both sides:
4 = x2
Using the second coordinate:
-1 = (4 + y2)/2
Multiply both sides of the equation by 2:
-2 = 4 + y2
Subtract 4 from both sides:
-6 = y2
Therefore, point B is located at (4, -6).
So the correct response is: (4, -6)