What is the distance between #(2,-4)# and #(-10,1)#?

2 Answers
Anjali_Sharma
Dec 30, 2015

The distance between #(2,-4)# and #(-10,1)# is #13 units.#

Trevor Ryan.
Dec 30, 2015

#13#

Explanation:

Assuming these 2 points, call them #x and y,# are in #RR^2# which is a complete metric space and a complete normed space, we may use either the normal Euclidean metric or the metric induced by the norm to evaluate the distance.

Normal Euclidean metric:

#d(x,y)=sqrt((x_1-x_2)^2+(y_1-y^2)^2)#

#=sqrt((2-(-10))^2+(-4-1)^2)#

#=13#.

#Metric induced by the norm:

#d(x,y)=||x-y||#

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

#=13#.

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