# For points A: (1,5) and B: (5,8) Find: a) distance from A to B b) the coordinates of the...

## Question:

For points A: (1,5) and B: (5,8) Find:

a) distance from A to B

b) the coordinates of the mid-point of AB

## distance

The distance can be represented as the span which exists any 2 points and distance exits in any one plane either it is XZ, ZY, YX distance is 2d quantity . and measured in m, cm, km, nm. Distance generally used for showing space between two places like the distance between point d to w is 4km.

A) For distance between A and B

Formula =

{eq}\begin{align*} {\rm{S = }}\sqrt {{{\left( {{{\rm{Q}}_{\rm{2}}}{\rm{ - }}{{\rm{Q}}_{\rm{1}}}} \right)}^{\rm{2}}}{\rm{ + }}{{\left( {{{\rm{T}}_{\rm{2}}}{\rm{ - }}{{\rm{T}}_{\rm{1}}}} \right)}^{\rm{2}}}} \\ {\rm{here,}}\\ {{\rm{Q}}_{\rm{2}}}{\rm{ = 5}}\\ {{\rm{Q}}_{\rm{1}}}{\rm{ = 1}}\\ {{\rm{T}}_{\rm{2}}}{\rm{ = 8}}\\ {{\rm{T}}_{\rm{1}}}{\rm{ = 5}}\\ {\rm{Putting}}\;{\rm{values}}\;{\rm{in}}\;{\rm{above}}\;{\rm{formula}}\\ {\rm{S = }}\sqrt {{{\left( {{\rm{5 - 1}}} \right)}^{\rm{2}}}{\rm{ + }}{{\left( {{\rm{8 - 5}}} \right)}^{\rm{2}}}} \\ {\rm{S = }}\sqrt {{{\left( {{\rm{5 - 1}}} \right)}^{\rm{2}}}{\rm{ + }}{{\left( {{\rm{8 - 5}}} \right)}^{\rm{2}}}} \\ {\rm{S = }}\sqrt {{\rm{16 + 9}}} \\ {\rm{S = }}\sqrt {25} \\ {\rm{S = 5}} \end{align*} {/eq}

B) For midpoint between A and B

{eq}\begin{align*} \left( {{\rm{Q',T'}}} \right)\\ {\rm{Q' = }}\dfrac{{{{\rm{Q}}_{\rm{1}}}{\rm{ + }}{{\rm{Q}}_{\rm{2}}}}}{{\rm{2}}}\\ {\rm{T' = }}\dfrac{{{{\rm{T}}_{\rm{1}}}{\rm{ + }}{{\rm{T}}_{\rm{2}}}}}{{\rm{2}}}\\ {\rm{putting}}\;{\rm{values}}\;{\rm{in}}\;{\rm{above}}\,{\rm{fromula}}\\ {\rm{Q' = }}\dfrac{{{\rm{5 + 1}}}}{{\rm{2}}} = 3\\ {\rm{T' = }}\dfrac{{{\rm{5 + 8}}}}{{\rm{2}}} = \dfrac{{13}}{2} = 6.5\\ \left( {{\rm{3,6}}{\rm{.5}}} \right) \end{align*} {/eq}

The midpoint coordinate would be (3,6.5)