What is the distance between #(-7, 7) # and #(5, 6) #?

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Answer 1 · 2017-02-10T20:41:42

The distance between the two points is:

# sqrt(145)~~12.04# to 2 decimal places.

When you are not sure of something make a quick sketch so you can see more clearly what the situation is.

Tony B

Let point 1 be #P_1->(x_1,y_1)=(-7,7)#
Let point 2 be #P_2->(x_2,y_2)=(5,6)#
Let the direct distance between the two points be #d#

The change in down is: #""y_2-y_1" "=" "7-6" "=" "1#
The change in along is: #""x_2-x_1" "=" "5-(-7)" "=" " 12#

Using Pythagoras #d^2=12^2+1^2#

#d=sqrt(145)#

The only factors of 145 are 1, 5, 9, 145,

So we can not break this down into simplified surds (roots)

So we represent the solution as #sqrt(145)# which is an exact value or as a rounded decimal which is not exact.

#=> d= sqrt(145)~~12.04# to 2 decimal places.

The sign of #~~# means approximately