splash screen. concept label your diagram with the following new points: d e f g
TRANSCRIPT
Label your diagram with the following new points:
Which segment do you think would measure the distance between point C and ? (multiple choice)
A) B) C) D)
DE
FG
CORRECT ANSWER:
B)
The construction of a line perpendicular to an existing line through a point not on the existing line in Extend Lesson 1-5 establishes that there is at least one line through a point, P, that is perpendicular to a line, . The following postulate states that this line is the only line through P perpendicular to .
In other words, if you have a line,aand have a point not on the line,
Wthen there is only one line that exists that is perpendicular to theoriginal line that goes through the point.
Construct Distance From Point to a Line
A. A certain roof truss is designed so that the center post extends from the peak of the roof (point A) to the main beam. Construct and name the segment whose length represents the shortest length of wood that will be needed to connect the peak of the roof to the main beam.
A
Main Beam
ANSWER: The shortest length willalways be found byusing the segment thatis perpendicular
X
B. Which segment represents the shortest distance from point A to DB?
ANSWER: The shortest length willalways be found byusing the segment thatis perpendicular
Extra Examples
1. Given triangle ABC, draw the shortest distance from A to .
2. Given the pentagon, draw the shortest distance from A to .
A
B
C
A
B
C
DE
By definition, parallel lines do not intersect. An alternate definition states that two lines in a plane are parallel if they are everywhere equidistant. Equidistant means that the distance between two lines measured along a perpendicular line to the lines is always the same. This leads to the definition of the distance between two parallel lines.
Find the distance between each pair of parallel lines with the given equations.
2
a) y = 2 y = 3
b) x = 9 x = 1
c) y = -5 y = 7
d) x = 4 x = -6
COORDINATE GEOMETRY A. Line s contains points at (0, 0) and (–5, 5). Find the distance between line s and point V(1, 5).
Distance from a Point to a Line on Coordinate Plane
(–5, 5)
(0, 0)
V(1, 5)
COORDINATE GEOMETRY B. Line n contains points (2, 4) and (–4, –2). Find the distance between line n and point B(3, 1).
Distance Between Parallel Lines
A. Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x – 1, respectively.
b a
p
B. Find the distance between the parallel lines a and
b whose equations are and ,
respectively.