Question 293363

Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(0,6\right)]. So this means that {{{x[1]=0}}} and {{{y[1]=6}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-2,6\right)].  So this means that {{{x[2]=-2}}} and {{{y[2]=6}}}.



{{{d=sqrt((x[1]-x[2])^2+(y[1]-y[2])^2)}}} Start with the distance formula.



{{{d=sqrt((0--2)^2+(6-6)^2)}}} Plug in {{{x[1]=0}}},  {{{x[2]=-2}}}, {{{y[1]=6}}}, and {{{y[2]=6}}}.



{{{d=sqrt((2)^2+(6-6)^2)}}} Subtract {{{-2}}} from {{{0}}} to get {{{2}}}.



{{{d=sqrt((2)^2+(0)^2)}}} Subtract {{{6}}} from {{{6}}} to get {{{0}}}.



{{{d=sqrt(4+(0)^2)}}} Square {{{2}}} to get {{{4}}}.



{{{d=sqrt(4+0)}}} Square {{{0}}} to get {{{0}}}.



{{{d=sqrt(4)}}} Add {{{4}}} to {{{0}}} to get {{{4}}}.



{{{d=2}}} Take the square root of {{{4}}} to get {{{2}}}.



So our answer is {{{d=2}}} 



So the distance between the two points is  2 units. 



Note: If you plot the two points on a coordinate grid, you can easily count the number of spaces between the two points to be 6 units. However, this method only works if the two points have either the same x coordinate or the same y coordinate.