How do you find the distance between #(0, -4)# and #(4,4)#?

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Answer 1 · 2017-06-21T14:43:10

#4sqrt(5)#

Distance = #sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)#

Plug your points into the formula.

You can make either coordinate set #1. Let's use (0, -4) as our first.

#(0, -4) #
#x_1 = 0, y_1 = -4#

#(4, 4)#
#x_2 = 4, y_2 = 4#

Distance = #sqrt((4 - 0)^2 + (4 - (-4))^2)#

#= sqrt(4^2 + 8^2)#
#= sqrt(16 + 64)#
# = sqrt(80)#
# = sqrt(5)*sqrt(16)#
# = sqrt(5)*4#
# = 4sqrt(5)#

The distance between the two points is #4sqrt(5)#.