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What is the distance between # (–2, 1, 3) # and #(–4, 0, 2) #?

Answer 1

Nathan Axel

The distance between (–2, 1, 3) and (–4, 0, 2) is approximately 2.449 units.

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Answer 2

Isaiah Anthony

See the entire solution process below:

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 + (color(red)(z_2) - color(blue)(z_1))^2)#

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(-4) - color(blue)(-2))^2 + (color(red)(0) - color(blue)(1))^2 + (color(red)(2) - color(blue)(3))^2)#

#d = sqrt((color(red)(-4) + color(blue)(2))^2 + (color(red)(0) - color(blue)(1))^2 + (color(red)(2) - color(blue)(3))^2)#

#d = sqrt((-2)^2 + (-1)^2 + (-1)^2)#

#d = sqrt(4 + 1 + 1)#

#d = sqrt(6) = 2.449# rounded to the nearest thousandth.

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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.