What is the distance between # (-4, 11)# and #(5, 6) #?

1 Answer
Shantelle
Jul 25, 2018

The distance is #sqrt106# or about #10.296# (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((5-(-4))^2 + (6-11)^2)#

Now we simplify:
#d = sqrt((9)^2 + (-5)^2)#

#d = sqrt(81 + 25)#

#d = sqrt(106)#

If you want to leave it in exact form, you can leave the distance as #sqrt106#. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
#d ~~ 10.296#

Hope this helps!

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