the midpoint of a line segment is (3,4). one of the endpoints of that line segment is (7,4). what is the other endpoint?
let the other endpoint be (a,b)
by the midpoint method:
(a+7)/2 = 3
a+7 = 6
a = -1
(b+4)/2 = 4
b+4 = 8
b = 4
the other point is (-1,4)
To find the other endpoint of the line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two endpoints (x1, y1) and (x2, y2) is given by the average of the x-coordinates and the average of the y-coordinates.
Let the coordinates of the other endpoint be (x, y). We know that the midpoint of the line segment is (3, 4) and one of the endpoints is (7, 4).
Using the midpoint formula, we can set up the following equations:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
Substituting the given values:
3 = (x + 7) / 2
4 = (y + 4) / 2
To solve for x, we can multiply both sides of the first equation by 2 and subtract 7:
6 = x + 7 - 7
6 = x
Therefore, the x-coordinate of the other endpoint is 6.
To solve for y, we can multiply both sides of the second equation by 2 and subtract 4:
8 = y + 4 - 4
8 = y
Therefore, the y-coordinate of the other endpoint is 8.
Thus, the other endpoint of the line segment is (6, 8).