what is the equation of the locus points equidistant from the lines y=1 and x=2
Can you figure it out from this?:
Locus Theorem 5: (intersecting lines)
The locus of points equidistant from two intersecting lines, l1 and l2, is a pair of bisectors that bisect the angles formed by l1 and l2 .
To find the equation for the locus of points equidistant from the lines y = 1 and x = 2, we need to determine the points that are equidistant from both lines.
Let's start with the horizontal line y = 1. Any point on this line will have its y-coordinate as 1. In other words, the distance between any point (x, y) on the line y = 1 and the line y = 1 itself is simply |y - 1|.
Next, we consider the vertical line x = 2. Any point on this line will have its x-coordinate as 2. Therefore, the distance between any point (x, y) on the line x = 2 and the line x = 2 itself is |x - 2|.
Since we want the points that are equidistant from both lines, we can set up the following equation:
|y - 1| = |x - 2|
To simplify this equation, we will consider two cases:
1. When (y - 1) and (x - 2) are both non-negative:
In this case, the equation becomes:
y - 1 = x - 2
2. When (y - 1) is non-negative and (x - 2) is negative:
In this case, the equation becomes:
y - 1 = -(x - 2)
To find the locus points, we can solve these two equations separately.
1. Solving y - 1 = x - 2:
Rearranging the equation, we get:
x - y = 1
2. Solving y - 1 = -(x - 2):
Rearranging the equation, we get:
x + y = 3
Therefore, the two equations we found represent the locus of points equidistant from the lines y = 1 and x = 2.