Locus question help (1 Viewer)

[Baranxyz]

Find the equation of the locus of a point P(x,y) that is subject to the following condition:
The distance of a point from the line x=4 is equal to its distance from the line y=1.

How do I approach this question? I have tried equating the distances of the points, and was unsuccessful. I don't know if i'm doing it incorrectly, or if there's another approach to the question.

Thanks in advanced .

Answer: x-y-3=0, x+y-5=0

 

[Drongoski]

Find the equation of the locus of a point P(x,y) that is subject to the following condition:
The distance of a point from the line x=4 is equal to its distance from the line y=1.

How do I approach this question? I have tried equating the distances of the points, and was unsuccessful. I don't know if i'm doing it incorrectly, or if there's another approach to the question.

Thanks in advanced .

Answer: x-y-3=0, x+y-5=0

P(x,y) is equidistant from x = 4 and from y = 1

.: distance of P from y = 1 = distance of P from x = 4

.: square of distance of P from y = 1 = square of distance of P from x = 4

.: (y - 1)² = (x - 4)²

.: y - 1 = +/- (x - 4)

.: the locus consists of the 2 lines:

i) y = x - 3

ii) y = -x + 5

 

[Baranxyz]

I see, I expanded the squares. I didn't think of square rooting both sides. Thank you.

 

[Drongoski]

For your next question: locus of point P(x,y) that is sqrt(2) from the line y = x.

If you are familiar with the perpendicular distance formula of a point from a given straight line, with equation given in the general form: