What is the distance between #(23,43)# and #(34,38)#?

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Answer 1 · 2018-07-10T14:00:54

See a 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)#

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(34) - color(blue)(23))^2 + (color(red)(38) - color(blue)(43))^2)#

#d = sqrt(11^2 + (-5)^2)#

#d = sqrt(121 + 25)#

#d = sqrt(146)#

Or, approximately:

#d ~= 12.083#

Answer 2 · 2018-07-11T00:05:07

#~~12.08#

The key realization is that we can use the distance formula

#sqrt((Deltax)^2+(Deltay)^2)#

Where the Greek letter Delta means "change in". We just need to figure out how much our #x# and #y# change by, respectively.

We go from #x=23# to #x=34#, so we can say #Deltax=11#.

We go from #y=43# to #y=38#, so we can say #Deltax=-5#.

Plugging these into our formula, we get

#sqrt((11)^2+(-5)^2)#

#=>sqrt(121+25)=sqrt(146)~~12.08#

Hope this helps!