What is the distance between #(-2,1)# and # (3,7) #?

1 Answer
Dec 7, 2015

Answer:

The distance between #(-2, 1)# and #(3, 7)# is #sqrt61# units.

Explanation:

We can use the distance formula to find the distance between any two given points, where #d =#the distance between the points #(x_1, y_1)# and #(x_2, y_2)#:

#d = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)#

If we plug in our points, our equation will be:

#d = sqrt((3-(-2))^2 + (7-1)^2)#

This can be simplified to #d = sqrt((5)^2 + (6)^2#

And then: #d = sqrt((25) + (36)#, which is #d = sqrt(61)#.

You can't simplify this further, so your final answer is #sqrt61# units.

Usually, the square root of a quantity would be #+# or #-# , but in this case, the quantity is only positive because it represents distance, which can never be negative.