P is a moving point in a rectangular coordinate plane such that the perpendicular distance from P to L1:x=3 is equal to that from P to L2:y=3.Suppose the locus of P is denoted by F and the slope of F is negative
a.)Describe the geometric relationship among F,L1 andL2.
b.)Find the equation of F
+23247 The locus of points in a plane that are equally distant to two intersecting lines are lines which are the two bisectors of the given lines. (The distance from a point to a line is found by measuring along the perpendicular to the line.)
Since L1 is vertical and L2 are horizontal, the bisectors will be the two lines which have slopes of 45° (m = 1) and 135° (m = -1).
For this problem, you want the line that passes through the intersection point of the two lines (3, 3) with a slope of -1; defined by the equation y = -x + 6.
You can debate whether or not you want the point (3,3) included in the locus (Is a distance of 0 really a distance?); my preference is to include it.
+23247 The locus of points in a plane that are equally distant to two intersecting lines are lines which are the two bisectors of the given lines. (The distance from a point to a line is found by measuring along the perpendicular to the line.)
Since L1 is vertical and L2 are horizontal, the bisectors will be the two lines which have slopes of 45° (m = 1) and 135° (m = -1).
For this problem, you want the line that passes through the intersection point of the two lines (3, 3) with a slope of -1; defined by the equation y = -x + 6.
You can debate whether or not you want the point (3,3) included in the locus (Is a distance of 0 really a distance?); my preference is to include it.
+128707 Here's a graph that might help explain what geno is describing.......
https://www.desmos.com/calculator/rgris7izxp
Note that the diagonal lines, y= x and y =-x + 6, create a set of points ( a "locus' ) that are all equi-distant from the lines x = 3 and y = 3.
But the one that we're interested in is the one with the negative slope, y = -x + 6, which goes through the point (3,3).
{I agree with geno, (3,3) should be included!! }
+118613 I am sorry but I just don't get this question.
What does
L1:x=3 mean? Is it some weird ratio?
Is the distance 3 units, if so then it should be 3 units all the time not just at one point.
To me this question does simply does not make any sense. 
+118613 okay NOW I have worked out what the question is!!!!!
P is a moving point in a rectangular coordinate plane such that the perpendicular distance from P to L1:x=3 is equal to that from P to L2:y=3.Suppose the locus of P is denoted by F and the slope of F is negative
INTERPRETATION
L1 is the line x=3, L2 is the line y=3
P is a moving point in a rectangular coordinate plane such that the perpendicular distance from P to L1 is equal to that from P to L2 Suppose the locus of P is denoted by F and the slope of F is negative
a.)Describe the geometric relationship among F,L1 andL2.
b.)Find the equation of F
a.)Describe the geometric relationship among F,L1 andL2.
b.)Find the equation of F
