The midpoint of line segment AB is (3, -1). Point A is at (2, 4). Where is point B located? Responses (5, -4) (5, -4) (4, -6) (4, -6) (52,32) open paren 5 halves comma 3 halves close paren (-2, 5)
To find the location of point B, given that point A is at (2, 4) and the midpoint is at (3, -1), we utilize the midpoint formula, which is the average of the x-coordinates and y-coordinates of points A and B.
Given the midpoint M(x, y), and point A(x1, y1), the coordinates of point B(x2, y2) are found using the equations:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
Plugging the known values for the midpoint M and point A, we have:
3 = (2 + x2) / 2
-1 = (4 + y2) / 2
Let's solve for x2 and y2:
For x2:
3 = (2 + x2) / 2
6 = 2 + x2 (after multiplying both sides by 2)
x2 = 6 - 2
x2 = 4
For y2:
-1 = (4 + y2) / 2
-2 = 4 + y2 (after multiplying both sides by 2)
y2 = -2 - 4
y2 = -6
Therefore, the coordinates for point B are (4, -6).
The correctly provided options in your list are:
(4, -6)
(4, -6)