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

2 Answers
Dec 30, 2015

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

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.