What is the distance between # (2, 5) # and # ( 7, 4) #?

1 Answer
Shantelle
Jul 25, 2018

The distance is #sqrt26# or about #5.099# (rounded to nearest thousandth's place).

Explanation:

The formula for the distance of 2-dimensional coordinates is: #d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)#

We have the two coordinates, so we can plug in the values for #x# and #y#:
#d = sqrt((7-2)^2 + (4-5)^2)#

Now we simplify:
#d = sqrt((5)^2 + (-1)^2)#

#d = sqrt(25 + 1)#

#d = sqrt(26)#

If you want to leave it in exact form, you can leave the distance as #sqrt26#. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
#d ~~ 5.099#

Hope this helps!

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