Question 120516
To find the distance between two points, use the distance formula:


{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}}


In your case, for the points given:


{{{d=sqrt(((-1)-(-1+3*sqrt(3)))^2+(1-4)^2)}}}


{{{d=sqrt((3*sqrt(3))^2+(-3)^2)}}}


{{{d=sqrt(27+9)=sqrt(36)=6}}}


The x-coordinate of the midpoint between two points is given by {{{(x[2]-x[1])/2}}}, or in this case {{{x[m]=((-1+3*sqrt(3))-(-1))/2=(3*sqrt(3))/2}}}


Likewise, the y-coordinate is given by: {{{(y[2]-y[1])/2}}}, in this case, {{{y[m]=(4-1)/2=3/2}}}


Therefore, the midpoint is ({{{(3*sqrt(3))/2}}},{{{3/2}}})