Name:
Unit 1: Introduction to Geometry
CRS
Level
Level 1
Review: 13-23
Review
NCP: Exhibit knowledge of
elementary number concepts
including rounding, the ordering
of decimals, pattern
identification, absolute value,
primes, and greatest common
factor
Period:
Date:
Section 1.3: Distance and Midpoint (Honors)
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: 24-27
GR: Find the midpoint of a
segment
Extension: 28-32
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 –
Worksheet
Directions: Simplify the following expressions.
1. |−9 + 6|
2. |−12 − 1|
3. |8 − (−1)|
1
4. |−4 − 1 + 5|
5. |𝑥 − 7| when 𝑥 = 2
6. |−3𝑥 + 1| when 𝑥 = 5
7. |5𝑥 − (−2)| when 𝑥 = 4
Level 2:
Practice:
Congruence of line segments
Page 26
Line segments that have the same length are called____________________________.
The symbol ≅ means “is congruent to.” Tick marks represent congruency on segments.
Lengths are equal: 𝐴𝐵 = 𝐶𝐷
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅
Segments are congruent: 𝐴𝐵
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. 𝐶𝐸
2. ̅̅̅̅
𝐷𝐺
̅̅̅̅
3. 𝐵𝐹
2
#31-42, 54
̅̅̅̅
4. 𝐶𝐺
5. ̅̅̅̅
𝐴𝐵
Midpoint on a coordinate plane
If a segment has endpoints with coordinates ( x1 , y1 ) and ( x2 , y2 ) then the formula for the midpoint is
 x1  x 2 y1  y 2 
,

2 
 2
Midpoint = 
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
Symbols
̅̅̅̅ is the point between P and Q such that
The midpoint M of 𝑷𝑸
PM=MQ
Number Line
Coordinate Plane
Models
3
Level 3:
Practice:
Distance on the number line
Page 25
#13-28
Directions: Use the number line to find each measure.
1. BD
2. DG
3. BF
4. CG
5. AG
Distance in the coordinate plane (Distance Formula)
The distance between two points in a coordinate plane can be found by using the
_____________________________.
If 𝐴(𝑥1 , 𝑦1 ) and 𝐵(𝑥2 , 𝑦2 )are points in the coordinate plane, then the distance between A and B is:
√(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
Directions: Find the approximate length of ̅̅̅̅
𝐴𝐵 (i.e. distance between A and B).
4
̅̅̅̅ for 𝐹(−3, −2) and 𝐺(1,1).
1. Find the length of 𝐹𝐺
2. Find the length of ̅̅̅̅
𝐷𝑆 for 𝐷(−2, −4) and 𝑆(4,4).
̅̅̅ for 𝑆(−1,2) and 𝑇(3, −2).
3. Find the length of ̅𝑆𝑇
Distance in the coordinate plane (Pythagorean Theorem)
The Distance Formula is based on the ___________________________________________.
Directions: Use the Pythagorean Theorem to find the distance between 𝐴(−2, −1) and 𝐵(1,3).
1. Use the Pythagorean Theorem to find the distance between 𝐹(−3, −2) and 𝐺(1,1).
5
2. Use the Pythagorean Theorem to find the distance between 𝐷(−2, −4) and 𝑆(4,4). (Hint: Sketch the
graph of the line segment).
̅̅̅ for 𝑆(−1,2) and 𝑇(3, −2). (Hint: Sketch the
3. Use the Pythagorean Theorem to find the length of ̅𝑆𝑇
graph of the line segment).
Summary:
Practice:
_____________________________________________________________________________
Page 25-27
Level 4
#12, 43-47, 55
& worksheet
Finding the coordinates of an endpoint of a segment (if you know the coordinates of its other endpoint
and its midpoint)
̅̅̅̅ and F has coordinates (-5, -3).
Directions: Find the coordinates of D if E(-6, 4) is the midpoint of 𝐷𝐹
Step 1: Substitute the given information into the Midpoint Formula.
Let 𝐹 = (𝑥2 , 𝑦2 )
Step 2: Write two equations to find the coordinates of D.
6
̅̅̅̅ and C has coordinates (-3, 6).
1. Find the coordinates of A if B(0, 5.5) is the midpoint of 𝐴𝐶
̅̅̅̅ and C has coordinates (-3, 6).
2. Find the coordinates of A if B(0, 5.5) is the midpoint of 𝐴𝐶
Using Algebra to find the measures of a segment
̅̅̅̅ if B is the midpoint of 𝐴𝐶
̅̅̅̅ ?
1. What is the measure of 𝐵𝐶
2. What is the measure of ̅̅̅̅
PR if Q is the midpoint of ̅̅̅̅
PR?
3. Points S, T, and P lie on a number line. Their coordinates are 0, 1, and x, respectively. Given 𝑆𝑃 = 𝑃𝑇,
what is the value of x?
𝑥
̅̅̅̅ 𝐽𝑀 = , and 𝐽𝐾 =
4. M is the midpoint of 𝐽𝐾,
8
3𝑥
4
− 6. Find MK.
5. The endpoints of ̅̅̅
𝐿𝐹̅ are 𝐿(−2,2) and 𝐹(3,1) . The endpoints of ̅̅̅
𝐽𝑅 are 𝐽(1, −1) and 𝑅(2, −3). What
is the approximate difference in the lengths of the two segments?
7
Midpoint and Segment Length Worksheet
Directions: Find the missing segment length. Then find the total length of the given line segment.
8
9