Question

A graph displays point A (5, 3, 4) and point B (−4, 2, 6). Calculate the approximate distance each point is from the origin. Round to the nearest tenth.

Answer 1

Given the two points
`P_(1)(x_(1), y_(1) , z_(1))` and
`P_(2)(x_(2), y_(2) , z_(2))` the distance d between these points is given by the formula:


`d = \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)+(z_(2)-z_(1))^(2)}`

Given that the problem ask for the distance A from the origin and B from the origin, we're going to calculate two distances:

Distance 1:


`P_(1) = P_(1)(0,0,0)`

`P_(2)=A(5, 3, 4)`

So:

`d_(1) = \sqrt{(5-0)^(2)+(3-0)^(2)+(4-0)^(2)}`

`d_(1) = 7.07`

Distance 2:


`P_(1) = P_(1)(0,0,0)`

`P_(2)=A(-4,2,6)`

So:

`d_(2) = \sqrt{(-4-0)^(2)+(2-0)^(2)+(6-0)^(2)}`

`d_(2) = 7.48`

Answer 2

The general formula for getting the distance between two points is. √(x²+y²+z²).

So the distance of A from the origin is;
√(5²+3²+4²) = √(25+3+16)
=√50
=7.1

The distance of B from the origin;
√((-4)²+2²+6²) = √(16+4+36)
= √80.28427125
=9.0