What is the approximate distance between point #(5,7)# and point #(-2, 3)#?

1 Answer
Jan 24, 2016

Approximately #8#

Explanation:

The distance between points #(x_1, y_1)# and #(x_2, y_2)# is given by the formula:

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

In our case, let #(x_1, y_1) = (5, 7)# and #(x_2, y_2) = (-2, 3)# and apply the formula to find:

#d = sqrt((5-(-2))^2 + (7-3)^2) = sqrt(7^2+4^2) = sqrt(49+16)#

#= sqrt(65)#

Now #8^2 = 64#, so #sqrt(65) ~~ 8#

Actually, #sqrt(65)# can be expressed as a very simple continued fraction:

#sqrt(65) = [8;bar(16)]=8+1/(16+1/(16+1/(16+...)))#

So a better approximation for #sqrt(65)# than #8# would be #8+1/16 = 8.0625#