Ms Andrejko Real World Vocabulary Equidistant the distance between two lines measured along a perpendicular line to the lines is always the same The distance between a line and a point not on the line is the length of the segment ID: 363955
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Slide1
3-6 Perpendiculars and Distance
Ms. AndrejkoSlide2
Real WorldSlide3
Vocabulary
Equidistant-
the distance between two lines measured along a perpendicular line to the lines is always the same
The distance between a line and a point not on the line is the length of the segment
perpendicular
to the line from the point.
The distance between two parallel lines is the
perpendicular distance
between one of the lines and any point on the other line. Slide4
Theorems & Postulates
Postulates
3.6
Theorem
3.9 –
Two Lines Equidistant from a Third-
in a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other. Slide5
Examples
Construct the segment that represents the distance indicated.Slide6
Examples
Construct the segment that represents the distance indicated.Slide7
Steps (when given line and pt.)
1. Find perpendicular slope
2. Make equation using perpendicular slope and given point (P)
3. Solve system of equations to find point of intersection
4. Plug into distance formulaSlide8
Examples
Find the distance from P to ℓ.
Line ℓ
y
=-x-2. Point P has coordinates (2, 4)
Perpendicular slope:
Equation through point:
System of equations:
Distance formula:
m
=1
y-4 = 1(x-2)
y-4 = x-2
y
=x+2
-x-2=x+2
-2=2x+2
-4=2x
-2=
x
y
=x+2
y
=-2+2
y
=0
(-2,0)
√(-2-2)
2
+(0-4)2√(-4)2+(-4)2√16+16
√32 = 4√2Slide9
Practice
Find the distance from P to ℓ.
Line ℓ
y
=-
x
. Point P has coordinates (1, 5)
Perpendicular slope:
Equation through point:
System of equations:
Distance formula:
m
=1
y-5 = 1(x-1)
y-5 = x-1
y
= x+4
-
x
= x+4
-2x=4
x
=-2
y
=-2+4
y
=2
(-2,2)
√(-2-1)
2+(2-5)2√(-3)2+(-3)2√9+9
√18 = 3√2Slide10
Example
Find the distance from P to ℓ.
Line ℓ
y
=(4/3)x-2. Point P has coordinates (-1, 5)
Perpendicular slope:
Equation through point:
System of equations:
Distance formula:Slide11
Practice
Find the distance from P to ℓ.
Line ℓ
y
=-3x+8. Point P has coordinates (-1,1)
Perpendicular slope:
Equation through point:
System of equations:
Distance formula:Slide12
Steps (when given 2
parallel equations)
1. Find
y
-intercept of line
m
2. Write equation of perpendicular line through
y
-intercept (line
p
).
3. Use systems of equations to determine point of intersection between
l and p.4
. Use distance formulaSlide13
Examples
Find the distance between each pair of parallel lines with the given equations.
y
=5x-22
y
=5x+4 Slide14
Practice
Find the distance between each pair of parallel lines with the given equations.
y
=-3x+3
y
=-3x-17