Answered: "Distance between (4,2,2) and (5,-3,-1)?"

Jenny Stafford

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2022-08-16

Distance between (4,2,2) and (5,-3,-1)?

Answer & Explanation

pokajalaq1

Beginner2022-08-17Added 18 answers

Imagine a strong light directly above the line such that the z-axis is vertical and the xy-plane is horizontal. The line would cast a shadow onto the xy-plane (Projected image) and it would in all likelihood form a triangle with the x and y axis.
You could use Pythagoras to determine the length of this projection. You could again use Pythagoras to find the true length but this time the z-axis being as if it is the opposite and the projection being the adjacent.
By going through this process you will find that the final equation boils down to:
Let the distance between the points be d

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

d = \sqrt{1^{2} + {(- 5)}^{2} + {(- 3)}^{2}}

d = \sqrt{35}

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