What is the distance between #(-8,1,-3)# and #(1,4,2)#?

Answer 1

#sqrt115#

#(x,y,z)&(a,b,c)# the distance formula is #d=sqrt((x-a)^2+(y-b)^2+(z-c)^2)# so #d=sqrt((-8-1)^2+(1-4)^2+(-3-2)^2)# #=sqrt(81+9+25)# #=sqrt115#

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Answer 2

Eli Assouline

The distance between (-8,1,-3) and (1,4,2) is 10.44 units.

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Answer 3

Hazel Anglin

To find the distance between two points ( P_1(x_1, y_1, z_1) ) and ( P_2(x_2, y_2, z_2) ) in three-dimensional space, we use the distance formula:

[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} ]

Given points ( P_1(-8, 1, -3) ) and ( P_2(1, 4, 2) ), we substitute the coordinates into the formula:

[ d = \sqrt{(1 - (-8))^2 + (4 - 1)^2 + (2 - (-3))^2} ]

[ d = \sqrt{(1 + 8)^2 + (4 - 1)^2 + (2 + 3)^2} ]

[ d = \sqrt{9^2 + 3^2 + 5^2} ]

[ d = \sqrt{81 + 9 + 25} ]

[ d = \sqrt{115} ]

Therefore, the distance between the points (-8, 1, -3) and (1, 4, 2) is ( \sqrt{115} ) or approximately 10.72 units.

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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.