Question

The endpoints of a line segment are at the coordinates (3, -4, 6) and (5, 7, -2). What is the midpoint of the segment?

A. 7, 18, -10

B. 1.5, -2, 3

C. 1, -15, 14

D. 4, 1.5, 2

Answer 1

D.(4,1.5,2)

Explanation:

We have given two end-points of the line segment.

Let (x₁,y₁,z₁) = (3,-4,6) and (x₂,y₂,z₂) = (5,7,-2)

We have to find the mid-point of the line segment.

The formula to calculate mid-point is :

M = (x₁+x₂/2,y₁+y₂/2,z₁+z₂/2)

Putting given values in above formula, we have

M = (3+5/2,-4+7/2,6-2/2)

M = (8/2,3/2,4/2)

M = (4,1.5,2)

Hence, mid-point of the line segment is (4,1.5,2).

Answer 2

The answer is (D) ⇒ (4 , 1.5 , 2)

Explanation:

∵ the mid point = [(x1 + x2)/2 , (y1 + y2)/2 , z1 + z2)/2]

∵ x1 = 3 , x2 = 5

∵ y1 = -4 , y2 = 7

∵ z1 = 6 , z2 = -2

∴ (x1 + x2)/2 = (3 + 5)/2 = 4

∴ (y1 + y2)/2 = (-4 + 7)/2 = 1.5

∴ (z1 + z2)/2 = (6 + -2)/2 = 2

∴ The mid point of the segment is (4 , 1.5 , 2)