What is the distance between #(2,5) # and #(9,1)#?

1 Answer
Dec 9, 2015

Answer:

#color(white)(xx)sqrt65#

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)1-color(red)5)^2+(color(red)9-color(red)2)^2)#
#color(white)(xxx)=sqrt(color(red)4^2+color(red)7^2)#
#color(white)(xxx)=sqrt(color(red)16+color(red)49)#
#color(white)(xxx)=sqrt65#