The endpoints of a line segment are at the coordinates (4, -2, 5) and (6, 4, -3). What is the midpoint of the segment?
(-2, -6, 8)
(10, 2, 2)
(5, 1, 1)
(-1, -3, 4)
My choice- C
(4,-2,5), (x,y,z), (6,4,-3).
x-4 = (6-4)/2 = 1, X = 5.
y-(-2) = (4-(-2))/2 = 3, Y = 1.
z-5 = (-3-5)/2 = -4, Z = 1.
To find the midpoint of a line segment, we average the coordinates of the endpoints. Let's calculate it:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2)
Midpoint = ((4 + 6) / 2, (-2 + 4) / 2, (5 + -3) / 2)
Midpoint = (10 / 2, 2 / 2, 2 / 2)
Midpoint = (5, 1, 1)
Therefore, the midpoint of the line segment is (5, 1, 1), which matches option C.
To find the midpoint of a line segment, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint are the average of the corresponding coordinates of the two endpoints.
The given endpoints are (4, -2, 5) and (6, 4, -3). To find the midpoint, we need to find the average of the x, y, and z coordinates separately.
For the x-coordinate of the midpoint: (4 + 6) / 2 = 10 / 2 = 5
For the y-coordinate of the midpoint: (-2 + 4) / 2 = 2 / 2 = 1
For the z-coordinate of the midpoint: (5 + -3) / 2 = 2 / 2 = 1
Therefore, the midpoint of the line segment is (5, 1, 1).
So, your choice C, (5, 1, 1), is correct.