Download Name: Period: Date: Unit 1: Introduction to Geometry Section 1.3

Name:
Unit 1: Introduction to Geometry
CRS
Review: 13-19
EEI: Substitute whole numbers for
unknown quantities to evaluate
expressions
Period:
Date:
Section 1.3: Distance and Midpoint (PA)
Level
Level 1
Review
Objective
1. Students will be able to simplify absolute value expressions.
Level 2
Focus
2. Students will be able to find the midpoint on a number line and coordinate
plane.
Level 3
Extension
4. Students will be able to find the distance on a number line and coordinate
plane using the Distance Formula and Pythagorean Theorem.
Level 4
Extension
5. Students will be able to find the endpoints of a segment given the midpoint
and solve for variables given information about distance and midpoint.
Focus: 20-23
NCP: Exhibit knowledge of
elementary number concepts
including rounding, the ordering of
decimals, pattern identification,
absolute value, primes, and greatest
common factor
Extension: 24-27
GR: Find the midpoint of a segment
GR: Use the distance formula
PPF: Use the Pythagorean Theorem
CCSS
G-CO.1 Know precise definitions of
angle, circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions of
point, line, distance along a line, and
distance around a circular arc.
G-GPE.6 Find the point on a
directed line segment between two
given points that partition the
segment in a given ratio
Level 1:
Practice:
Absolute Value –
Assignment 1.3
Level 1
Absolute Value
Worksheet
Directions: Simplify the following expressions.
1.
5.
2.
3.
4.
7.
6.
1
Level 2:
Practice:
Congruence of line segments
Line segments that have the same length are called____________________________.
The symbol
means “is congruent to.” Tick marks represent congruency on segments.
Lengths are equal:
Segments are congruent:
Midpoint on a number line
If the coordinates of the endpoints of a segment are a and b, then the coordinate of the midpoint of the
segment is
Midpoint 
ab
2
Directions: Use the number line to find the coordinate of the midpoint of each segment.
1.
2.
3.
4.
5.
Midpoint on a coordinate plane
If a segment has endpoints with coordinates ( x1 , y1 ) and ( x2 , y2 ) then the formula for the midpoint
 x1  x 2 y1  y 2 
,

2 
 2
is Midpoint = 
2
Assignment 1.3
Level 2
Page 26
#31-40
Directions: Find the coordinates of the midpoint of a segment having the given endpoints.
1. E(-2, 6), F(-9, 3)
2. C(8, -6), B(-14, 12)
3. P(-1, 2), Q(6, 1)
Summary:
Words
The midpoint M of
is the point between P and Q such that
PM=MQ
Symbols
Number Line
Coordinate Plane
Models
Level 3:
Practice:
Distance on the number line
Assignment 1.3
Level 3
Page 25
#13-28
Directions: Use the number line to find each measure.
1. BD
2. DG
3. BF
4. CG
Distance in the coordinate plane (Distance Formula)
The distance between two points in a coordinate plane can be found by using the
3
5. AG
_____________________________.
If
is:
and
are points in the coordinate plane, then the distance between A and B
Directions: Find the approximate length of
1. Find the length of
2. Find the length of
for
for
(i.e. distance between A and B).
and
and
3. Find the length of
for
and
Distance in the coordinate plane (Pythagorean Theorem)
The Distance Formula is based on the ___________________________________________.
Directions:
1. Use the Pythagorean Theorem to find the
distance between
and
4
2. Use the Pythagorean Theorem to find the distance
between
and
3. Use the Pythagorean Theorem to find the distance between
the graph of the line segment).
3. Use the Pythagorean Theorem to find the length of
the graph of the line segment).
for
Summary:
5
and
and
(Hint: Sketch
(Hint: Sketch
Practice:
Level 4
Finding the coordinates of an endpoint of a segment (if you know the coordinates of its other
endpoint and its midpoint)
Directions: Find the coordinates of D if E(-6, 4) is the midpoint of
and F has coordinates (-5, -3).
Step 1: Substitute the given information into the Midpoint Formula.
Let
Step 2: Write two equations to find the coordinates of D.
1. Find the coordinates of A if B(0, 5.5) is the midpoint of
2. Find the coordinates of A if B(6, 3) is the midpoint of
and C has coordinates (-3, 6).
and C has coordinates (5, 4).
Using Algebra to find the measures of a segment
1. What is the measure of
if B is the midpoint of
?
2. What is the measure of
if Q is the midpoint of
?
6
Assignment 1.3
Level 4
Page 25-26
#12, 43,44, 46, 47
& worksheet
Midpoint and Segment Length Worksheet
Directions: Find the missing segment length. Then find the total length of the given line segment.
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8