find the distance between points....i have an answer, is it correct?

Question

find the distance between the points (a,b) and (b,a)

i basically used the distance formula/pythagorean theorem and i got:

sqrt( 2a^2 - 4ab + 2b^2) <----- is this the answer or is it

(+or-) sqrt( 2a^2 - 4ab + 2b^2)

Answer 1

the distance should be positive number, your answer is almost correct, it is : sqr (|2a^2 - 4ab + 2b^2|), i.e. take the sqr of the absolute value of (2a^2 - 4ab + 2b^2) .

Answer 2

distance is a scalar quantity & does not have sign. It is not negative. Therefore, sqrt( 2a^2 - 4ab + 2b^2) is the correct answer.

Answer 3

distance between the points (a,b) and (b,a)
distance = sqrtroot ( (b - a)^2 + (a -b)^2)
=sqrtroot( 2a^2 - 4ab + 2b^2)

Answer 4

the closest element will connect with the line with a line this is perpendicular to it. y = -2x + 7 has a slope of -2, so a line perpendicular could have a slope (a million/2) y = (a million/2)x + b 4 = (a million/2) * -6 + b 4 = -3 + b b = 7 y = (a million/2)x + 7 *** 6 = (a million/2) * -2 + b 6 = -a million + b b = 7 y = (a million/2)x + 7 Which makes those 2 factors collinear.

Answer 5

d = √ [ (x2 - x1)² + (y2 - y1)² ]
d = √ [ (b - a)² + (a - b)² ]
d = √ [ b² - 2ab + a² + a² - 2ab + b² ]
d = √ [ 2a² + 2b² - 4ab]
d = √ [ 2.(a² - 2ab + b²]
d = √ [ 2.(a - b)² ]
d = (√2).(a - b)
NB: d is a distance so will consider +ve square root value only.

Answer 6

Let A(x1,y1) and B(x2,y2) be two points.

dist (A,B)

= sqrt( (x1-x2)^2 + (y1-y2)^2)
Let x1 = a, y1 = b and x2 = b, y2 = a

Then,

Dist
= sqrt (( a-b)^2 + (b-a)^2)
= sqrt ( 2(a-b)^2)
or sqrt ( 2a^2 - 4ab + 2b^2)

positive distance (+)

Answer 7

is is + because distance is positive and sqrt(x) is defined to be positive..

for example sqrt(4) = + 2 but x^2 = 2 has x = +/- sqrt(2)

Answer 8

this is correct since distance is always positive
but it could be neater if you note (a-b)^2 = (b-a)^2
so
d= sqrt( (b-a)^2 + (a-b)^2 )
=sqrt( 2*(a-b)^2 )
= |a-b|*sqrt2

Answer 9

use the distance formula