SOLUTION: two sides of a square have the equation 5x+12y-10=0 and 5x+12y+29=0 the co-ordinates of a point on the third side(3,5).find the equation for the other two sides of square

Question 17135: two sides of a square have the equation 5x+12y-10=0 and 5x+12y+29=0
the co-ordinates of a point on the third side(3,5).find the equation for the other two sides of square
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
let ABCD be the square. let AB be given by 5x+12y-10=0 .the other equation given is 5x+12y+29=0 ...since ratios of x and y terms in both the lines are same (5/12 and 5/12),they represent parallel sides .so 5x+12y+29=0 represents the equation of CD.
since AD and BC should be perpendicular to the above lines ,their equations will be of the form 12x-5y+p=0 and 12x-5y+q=0.we are given that 3,5 lies on one of these .hence
12*3-5*5+p=0 or 36-25+p=0 or p=-11.
hence equation of AD or BC is 12x-5y-11=0 say let it be called AD.
to find the other equation , take any point on CD and find its distance from AB to determine the side of the square.
eqn.of CD is 5x+12y+29=0..take y=0 and then 5x+29=0 or x=29/5 ..so 29/5,0 is a point on CD.its distance from AB is given by
Side of square = [5*29/5+12*0-10]/=19/13
now BC should be at the same distance from AD.we know already that 3,5 is a point on AD as given in the problem.So let us find distance of 3,5 from BCand equate it to side of square = 19/13
19/13=(12*3-5*5+q)/=(11+q)/13(WE MAY TAKE BOTH PLUS AND MINUS SIGNS ON ONE SIDE OF THIS EQUATION TO GET THE 2 EQNS.OF BC WHICH COULD BE ON EITHER SIDE OF AD.)
11+q=19 or 11+q=-19
q=8 or -30
hence eqns.of BC are 12x-5y+8=0 or 12x-5y-30=0

RELATED QUESTIONS
The equation of the tangent line to the curve x^2 + y^2 =169 at the point (5,-12) is... (answered by jim_thompson5910)

the base of a triangle is given by the co-ordinates of the end points (0,0), (0,6). If... (answered by solver91311)

ABCD is a square. Point A has co-ordinates (2,4) and the line ODC has equation y=x. find (answered by josmiceli,venugopalramana)

find the shortest distance between the parallel lines with equations 5x-12y+33=0 and... (answered by jim_thompson5910,miker)

which has its center at the point (4:3)and touches the starting line 5x - 12y... (answered by ikleyn)

Please explain the steps to solve the following problem: y/4-y+5/3=0 i have changed... (answered by longjonsilver)

find the shortest distance between the parallel lines with equations... (answered by edjones)

for what value of a will the system of equation 4x+12y=-5, -5x+ay=8 have no solution -5 (answered by josgarithmetic)

i have a question if my multiple choice answers for my question find the shortest... (answered by jim_thompson5910,edjones)