Unit 1A – Distance and Midpoint (Notes)
Name:
Objective(s):
Key Concepts
Date:
Essential Question(s):
Notes
Distance
 Definition
Distance on a Number Line

What it looks like

Formula

Examples:
Distance on a Coordinate Plane
 What it looks like

Formula
Examples:
Find the distance between the
following ordered pairs:
1. R (5, 1) and S (-3, -3)
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Examples Continued:
Find the distance between the
following ordered pairs.
2. P (-4, 1) and Q (3, -1)
3. A (3, 4) and S (8, 0)
4. N (-2, -6) and M (-7, -5)
Midpoint
 Definition
Midpoint on a Number Line
 Formula
Examples:
5. Find the coordinate
of the midpoint of
PQ
6. The coordinates on a number
line of J and K are -6 and 8,
respectively. Find the
midpoint of JK .
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Midpoint on a Coordinate Plane
 Formula
Examples
7. Find the coordinates of the
midpoint of GH for G (8, -6)
and H (-14, 12).
8. Find the coordinates of M,
the midpoint of PQ for
(-1, 2) and Q (6, 1).
P
Sometimes you will be given the
midpoint and you will need to find
one of the endpoints.
9. Find the coordinates of X if Y
(-2, 2) is the midpoint of XZ
and Z has coordinates (2, 8).
(Hint: Draw a picture if you
need to.)
10. Find the coordinates of D if E
(6, 4) is the midpoint of DF
and F has coordinates (5, 3).
Segment Bisector
 Definition
Summary, Reflection, Analysis
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Unit 1A – Distance and Midpoints
Construction – Bisect a Segment
Name
Date
You can construct a line that bisects a segment without measuring to find the midpoint of
the given segment.
Construction – Bisect a Segment
1. Draw a segment and name it ̅̅̅̅
𝑋𝑌. Place the compass at point X. Adjust the compass
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so that its width is greater than 2 𝑋𝑌. Draw arcs above and below ̅̅̅̅
𝑋𝑌.
2. Using the same compass setting, place the compass at point Y and draw arcs above
and below ̅̅̅̅
𝑋𝑌 intersect the two arcs previously drawn. Label the points of the
intersection of the arcs as P and Q.
̅̅̅̅. Label the point where it intersects 𝑋𝑌
̅̅̅̅ as M.
3. Use a straightedge to draw 𝑃𝑄
Conclusion:
1. Point M is the _________________________ of ̅̅̅̅
𝑋𝑌.
2. Segment PQ is a _________________________ of ̅̅̅̅
𝑋𝑌.
3.
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2
𝑋𝑌 = ___________________ = __________________
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Unit 1A – Distance and Midpoints
Assignment #1
Name
Date
Write the Distance Formula:
Use the Distance Formula to find the distance between each pair of points.
1. A (0, 0) B (15, 20)
2. N (-12, 0) P (-8, 3)
3. C (11, -12) D (6, 2)
4. E (-2, 10) F (-4, 3)
5. G (-3, -4) H (5, 2)
6. Q (-3, 2) W (-2, -6)
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Unit 1A – Distance and Midpoints
Assignment #2
Name
Date
Write Midpoint Formula:
Use the number line below to find the coordinate of the midpoint of each segment
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Unit 1A – Distance and Midpoints
Assignment #3
Name
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For questions 4 and 5, construct two different size line segments and the
bisect them using only a compass and a straightedge.
4.
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5.
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Unit 1A – Distance and Midpoints
Name: __________________
Geometry Activity
Midpoint of a Segment
Model
̅̅̅̅.
 Graph points A (5, 5) and B (-1, 5) on grind paper. Draw 𝑨𝑩
 Hold the paper up to the light and fold the paper so that points A and B match
exactly. Crease the paper slightly.
 Open the paper and put a point where the crease intersects ̅̅̅̅
𝑨𝑩. Label this
midpoint as C.
 Repeat the first three steps using endpoints X (-4, 3) and Y (2, 7). Label the
midpoint Z.
Answer the following questions:
1. What are the coordinates of point C?
2. What are the lengths of ̅̅̅̅
𝑨𝑪 𝒂𝒏𝒅 ̅̅̅̅
𝑪𝑩 ?
3. What are the coordinates of point Z?
̅̅̅̅ 𝒂𝒏𝒅 𝒁𝒀
̅̅̅̅ ?
4. What are the lengths of 𝑿𝒁
5. What do you notice about the above segments?
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Unit 1A – Distance and Midpoints
Name: __________________
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Geometry Activity
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