What is the distance between #(5,-3)# and # (3,7) #?

1 Answer
Jul 25, 2018

Answer:

The distance is #2sqrt26# or about #10.198# (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((3 - 5)^2 + (7 - (-3))^2)#

Now we simplify:
#d = sqrt((-2)^2 + (10)^2)#

#d = sqrt(4 + 100)#

#d = sqrt(104)#

#d = 2sqrt26#

If you want to leave it in exact form, you can leave the distance as #2sqrt26#. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
#d ~~ 10.198#

Hope this helps!