What is the distance between #(8,5)# and #(1,2)#?

1 Answer
Júlio B.
Jan 3, 2016

#"distance"=sqrt(58)#

Explanation:

We can find this distance using Pythagoras' formula. But now we only have one side of the triangle, so, we need to complete the rectangle triangle, and in order to make a #pi/2# angle, we have to create two lines, one with the projection of the extremes in #x# axis, and the other with the projections in #y# axis. Then, we take the difference between the lines of both projections:
#trianglex = 8-1 = 7#
#triangley = 5-2 = 3#

Now, apply the formula: #"distance"^2 = 7^2 + 3^2#
#"distance"=sqrt(58)#

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