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

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