Download Analytic Geometry 2.4 Directed Distance From A Line To A Point

Analytic Geometry
2.4 Directed Distance From A
Line To A Point
Page 68
Objective: Find the Directed Distance from a
line to a point given the equation of the line
and the coordinates of the point.
Theorem 2.3
The directed distance from the slant line Ax + By + C = 0 to the point
P1 ( x1 , y1 ) is given by the formula
d=
Ax1  By1  C
,
 A B
where the denominator is given the sign of B. The distance is positive
2
2
if the point P is above the line, and negative if P is below the line.
Example 1
Find the distance from the
line 5x = 12y + 26 to the points P1(3, -5),
P2(-4,1), and P3(9, 0).
Example Two
Find the distance between the
parallel lines 15x + 8y + 68 = 0 and
15x + 8y -51 = 0.
Example Three
Find the equation of the bisector
of the pair of acute angles formed
by the lines x – 2y + 1 = 0
and x + 3y – 3 = 0.
Example Four
Find the equation of the bisector
of the pair of obtuse angles
of example three.
Additional Examples
Find the directed distance from
the line to the point.
12x + 5y – 6 = 0; (4, -6)
Additional Examples
Find the distance between the
two parallel lines.
3x – 4y – 9 = 0
3x – 4y + 3 = 0
Additional Examples
A circle has its center at (-4, -2) and
is tangent to the line 3x + 4y – 5 =
0. What is the radius of the circle?
What is the equation of the
diameter that is perpendicular to
the line?
Additional Examples
Find the equation of the bisector of
the acute angles and also the
equation of the bisector of the
obtuse angles formed by the lines
7x – 24y = 8 and 3x + 4y = 12.
Additional Examples
The vertices of a triangle are at A(3, -2), B(2,1), and C(6,5). Find the
length of the altitude from the
vertex C and the length of side AB.
Then compute the area of the
triangle.
Homework Assignment
Page 74 - 75
Problems 1 – 35 odd