Download 3 ___ Unit: Analytic Geometry Topic: _ Length of a Line Segment

Lesson Plan
Grade 10 Academic Math
Unit:
Lesson:
Analytic Geometry
3 - 3 ___
Topic: _ Length of a Line Segment
homework check: Principles of Mathematics 10 p. 72 #2, 4, 6, 7, 8,12, 15, 19
note: Length of a Line Segment
When you are finding the length of a line segment, you must remember the Pythagorean
Theorem. In the case of a line segment, we can use the rise and run as the length of the legs of
the diagonal. For example, find the length of segment AB.
A (-3, 4)
4
2
B (1, -1)
rise = 4 − ( −1)
=5
run = −3 − 1
= −4
c2 = a 2 + b2
c 2 = 5 2 + ( −4 )
2
c 2 = 25 + 16
c 2 = 41
c = 41
c = 6.4units
Notice that when working with the Pythagorean Theorem to find the length of the
hypotenuse of a triangle, we have used both finding the rise and run by subtracting and then
square rooting the sum. The distance formula puts all of these things together in one place as
follows:
d=
( x2 − x1 )
2
2
+ ( y2 − y1 ) . You should be able to see where each component of this formula
comes from.
Examples) Find the distance between the given points.
A ( −3.4 ) and B ( 2, −3)
d=
( −3 − 2 )
d=
( −5 )
2
2
+ ( 4 − ( −3) )
+ (7)
2
C (1, −8 ) and D ( −3, −2 )
2
d=
2
(1 − ( −3) ) + ( −8 − ( −2 ) )
d = 4 2 + ( −6 )
d = 25 + 49
d = 24 + 36
d = 74
d = 60
d = 8.6units
d = 7.7units
2
2
homework assignment: Principles of Mathematics 10 p. 86 # 5ii), 6, 9, 12, 13