What is the distance between #(1,5)# and #(2,12)#?

1 Answer
Dec 13, 2015

Answer:

#color(white)(xx)5sqrt2#

Explanation:

Let distance be #d#. Then:

#color(white)(xx)d^2=(Deltax)^2+(Deltay)^2color(white)(xxxxxxxxxxx)# (Pythagorous' Theorem)

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

#=>d=sqrt((color(red)2-color(red)1)^2+(color(red)12-color(red)5)^2)#
#color(white)(xxx)=sqrt(color(red)1^2+color(red)7^2)#
#color(white)(xxx)=sqrt(color(red)1+color(red)49)#
#color(white)(xxx)=5sqrt2#