1.3 – use midpoint and distance formulas & segment constructions
TRANSCRIPT
1.3 – Use Midpoint and Distance Formulas & Segment Constructions
Midpoint: Point in the middle of a segment
A BM
M is the midpoint of AB
MBAM
Segment bisector: Point, line, or segment that cuts a segment in half
A BM
pt. M bisects AB
MBAM
A BM
C
D
bisects ABCD
MBAM
Perpendicular: Line that intersects at a right angle
A B
C
D
CDAB
Perpendicular bisector: Perpendicular Line or segment that bisects a segment
A BM
C
D
CDAB
AM MB
Distance: Length between two points
AB
Measured in units
17cm 17cm
DF = 34cm
1. Line bisects the segment. Find the indicated length.
GJ = 16 12 in
1. Line bisects the segment. Find the indicated length.
2. M is the midpoint of the segment. Find the indicated length.
Find MF.
7x – 6 = 5x– 6 = -2x
3 = x
MF = 5(3) = 15u
2. M is the midpoint of the segment. Find the indicated length.
Find LN.
11x – 21 = 8x + 153x – 21 = 15
3x = 36x = 12
LN = 11(12)-21 + 8(12)+15
= 132 – 21 + 96 +15= 222u
3. Find the midpoint and distance of AB, where A(2, 5) and B(2, -3).
A
B
M
M(2, 1)
A
B
AB = 8u
3. Find the midpoint and distance of AB, where A(2, 5) and B(2, -3).
4. Find the midpoint and distance of AB, where A(-3, 4) and B(7, 4).
A BM M(2, 4)
A B
AB = 10u
4. Find the midpoint and distance of AB, where A(-3, 4) and B(7, 4).
5. Find the midpoint and distance of AB, where A(5, 8) and B(1, 2).
A
B
M M(3, 5)
A
B
5. Find the midpoint and distance of AB, where A(5, 8) and B(1, 2).
4
6
42 + 62 = c2
c16 + 36 = c2
52 = c2
132 = c
AB = 132 u
Midpoint Formula:
2,
22121 yyxx
Remember! Your answer should be an ordered pair!
Distance Formula:
2122
12 yyxxAB
Don’t forget your units!
6. Find the midpoint and distance of AB, where A(-6, 2)and B(-2, -3).
2,
22121 yyxx
1x 2x1y 2y
midpt AB =
14,2
6 2,
2
2 3
2
8,
2
1
2
2122
12 yyxxAB
41 u
(-2 – (-6))2+ (-3 – 2)2
(4)2 + (-5)2
16 + 25
6. Find the midpoint and distance of AB, where A(-6, 2)and B(-2, -3).1x 2x1y 2y
7. Find the midpoint and distance of AB, where A(-1, 2)and B(3, 4).1x 2x1y 2y
2,
22121 yyxx
midpt AB =
3,1
1 3,
2
2 4
2
2,2
6
2
2122
12 yyxxAB
20
52 u
(3 – (-1))2 + (4 – 2)2
(4)2 + (2)2
16 + 4
7. Find the midpoint and distance of AB, where A(-1, 2)and B(3, 4).1x 2x1y 2y
The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent.
P
Q
R
S
The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent.
2122
12 yyxxPQ 2122
12 yyxxRS
34 25
5Not
(-1 – 4)2 + (6 – 3)2
(-5)2 + (3)2
25 + 9
(-2 – 2)2 + (0 – (-3))2
(-4)2 + (3)2
16 + 9
HW Problem1.3 19-22 2, 3-21 odd, 24, 33, 37, 43, 57-59
What does the red circle mean around the problem number?
**Bring your protractor tomorrow!
# 15
x + 15 = 4x – 45 15 = 3x – 45 60 = 3x
20 = x
SU = 2(20+15)
SU = 2(35)
SU = 70u