Question 1081956
 The image of the point {{{A}}} ({{{1}}},{{{6}}}) when reflected in a line {{{PQ}}} is ({{{7}}},{{{6}}}). Write down the equation of the line {{{PQ}}}.

if the image of the point ({{{1}}},{{{6}}}) when reflected in a line {{{PQ}}} is ({{{7}}},{{{6}}}), line goes through midpoint of  A ({{{1}}},{{{6}}}) and  ({{{7}}},{{{6}}})


since A ({{{1}}},{{{6}}}) and  ({{{7}}},{{{6}}}) have same {{{y}}} coordinate, line that passes through is {{{horizontal}}} line {{{y=6}}}

coordinates of the midpoint will be:
{{{(1+7)/2}}}, {{{(6+6)/2}}})=({{{4}}},{{{6)}}}).... it is on {{{PQ }}} and on {{{y=6}}} as well

if so,  the line {{{PQ}}} must be {{{vertical}}} line {{{x=4}}}; {{{PQ=4}}}


{{{drawing( 600, 600, -10, 10, -10, 15,
line(4,-10,4,10), circle(1,6,.12), locate(1,6,A(1,6)),
circle(7,6,.12), locate(7,6,p(7,6)),
circle(4,6,.12), locate(4,6,p(4,6)),locate(4.2,4,PQ=4),
 graph( 600, 600, -10, 10, -10, 15, 6)) }}}