The coordinates of and of an equilateral are and respectively. is perpendicular to whereas the straight line is parallel to .Find
a)the equation of straight line
b)the coordinates of point
c)the equation of locus such that the distance of from point and are equal.
Since EG is perpendicular to FH, which has slope 1/2, EG has slope -2. That means that EG has equation y= -2(x- 3)+ 3.
Since FG is parallel to the x-axis, G must have the same y coordinate as F: -1. Solve -1= -2(x- 3)+ 3 to find the x coordinate.b)the coordinates of point
This is the straight line perpendicular to EF and passing through its midpoint. EF has slope (3-(-1))/(3- 0)= 4/3 so this line has slope -3/4. The midpoint of EF is ((3+(-1))/2, (3+ 0)/2).c)the equation of locus such that the distance of from point and are equal.