Question

A line segment has endpoint (5,4,3) and (1,6,-9) find it length and the midpoint g

Answer 1

Its squared length is given by the Pythagorean Theorem:

`d^2 = (5-1)^2 + (4-6)^2 + (3 - -9)^2 = 16 + 4 + 144 = 164`

`d = √(164) = 2√(41)`

Answer: 2√41

The midpoint is the average of each coordinate:

`G(x,y,z) = \left( (5 + 1)/(2), (4 + 6)/(2), (3 + -9)/(2) \right) = (3, 5, -3)`

Answer: (3, 5, -3)