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What is the distance between the origin and the point (-19, 6)?

Answer 1

Eva Adamson

The distance between the origin and the point (-19, 6) is 20.396078054371138.

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Answer 2

Hazel Anglin

The distance is #sqrt(397)# or 19.9 rounded to the nearest tenth.

The origin is point (0, 0). The formula for calculating the distance between two points is:

#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)#

Substituting the point given in the problem and the origin gives:

#d = sqrt((color(red)(0) - color(blue)(-19))^2 + (color(red)(0) - color(blue)(6))^2)#

#d = sqrt((color(red)(0) + color(blue)(19))^2 + (color(red)(0) - color(blue)(6))^2)#

#d = sqrt(19^2 + (-6)^2)#

#d = sqrt(361 + 36)#

#d = sqrt(397) = 19.9# rounded to the nearest tenth.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.