Question 1197077


The distance formula is:


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


given:

  ({{{x[1]}}}, {{{y[1]}}}) =({{{9}}}, {{{4}}}) 

 ({{{x[2]}}}, {{{y[2]}}}) = ({{{x}}},{{{- 8}}})

{{{d=13}}}


plug in distance formula:


{{{13=sqrt((x-9)^2+(-8-4)^2)}}}

{{{13=sqrt(x^2 - 18x + 225)}}}...........square both sides

{{{13^2=x^2 - 18x + 225}}}

{{{169=x^2 - 18x + 225}}}

{{{0=x^2 - 18x + 225-169}}}

{{{0=x^2 - 18x + 56}}}.........factor

{{{0=x^2 -4x- 14x + 56}}}

{{{0=(x^2 -4x)- (14x - 56)}}}

{{{0=x(x -4)-14 (x - 4)}}}

{{{ (x - 14) (x - 4)=0}}}


solutions:


if {{{ (x - 14) =0}}} =>{{{x=14}}}

if {{{ (x - 4) =0}}} =>{{{x=4}}}




the point ({{{x}}},{{{- 8}}}) could be:

({{{14}}},{{{- 8}}})

or

({{{4}}},{{{- 8}}})


answer: {{{4}}}, {{{14}}}


check the answer:


({{{9}}}, {{{4}}})  and ({{{14}}},{{{- 8}}})

*[invoke formula_distance 9, 4, 14, -8] 


and


({{{9}}}, {{{4}}})  and ({{{4}}},{{{- 8}}})

*[invoke formula_distance 9, 4, 4, -8]