The distance between the points (x, 21) and (4, -7) is 10*sqrt(3) . Find the sum of all possible values of x.
Just use distance formula between two points
(x-4)^2 + ( 21- -7)^2 = ( 10 sqrt3 )^2 Solve this for the values of 'x'
The distance formula is: d = sqrt( (x2 - x1)2 + (y2 - y1)2 )
Replacing: 10·sqrt(3) = sqrt( (4 - x)2 + (-7 - 21)2 )
Squaring: 300 = (4 - x)2 + (-7 - 21)2
300 = (4 - x)2 + (-28)2
300 = (4 - x)2 + 784
-484 = (4 - x)2
This is impossible.
