The document discusses finding the equation of a line that represents points equidistant from the lines y=5 and x=-4. It shows a diagram of the two lines on a coordinate plane, with the set of equidistant points forming a line at a 45 degree angle between the two original lines. The equation of the equidistant line is determined to be x + y = 1 based on the slope of -1 and the point (-4,5) where the two original lines intersect.

1. Coordinate Geometry

2. Coordinate Geometry
What is the equation of a set of points equidistant from the lines
y = 5 and x = –4?
(a) x + y = –1 (b) x – y = –1
(c) x + y = 1 (d) –x + y = –1

3. Coordinate Geometry
Let us try to draw
the given lines
on the coordinate
plane.
What is the equation of a set of points equidistant from the lines
y = 5 and x = –4?
(0, 0)
(-4, 5) y = 5
x = -4
(-4, 0)
(0, 5)
Y axis
X axis

4. Coordinate Geometry
Let us try to draw
the given lines
on the coordinate
plane.
What is the equation of a set of points equidistant from the lines
y = 5 and x = –4?
(0, 0)
(-4, 5) y = 5
x = -4
(-4, 0)
(0, 5)
Y axis
X axis
45o
45o
135o

5. Coordinate Geometry
A set of points equidistant from the given two lines should lie on the
dotted line as indicated. You can think of it as the perpendicular
bisector to the base of an isosceles triangle formed by (–4, 5) and the
two points on x = –4 and y = 5.
Or, the set of points equidistant from two lines form the angle
bisector of the angle formed at the point of intersection of the two
lines. The angle between these two lines is 900. Importantly, the
lines are parallel to the axes. So, thinking of the line that is the angle
bisector of this angle should not be too difficult.
What is the equation of a set of points equidistant from the lines
y = 5 and x = –4?

6. Coordinate Geometry
This dotted line is at an angle of 135o with respect to the positive
direction of x–axis and also passes through (–4, 5).
Slope = m = tan (135o) = –1.
Therefore, the equation is given by (y – y1) = m
(x – x1) where (x1, y1) is (–4, 5).
(y – 5) = –(x + 4)
x + y = 1
Answer choice (c)
What is the equation of a set of points equidistant from the lines
y = 5 and x = –4?

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