Transcript Glencoe Geometry

Five-Minute Check (over Lesson 1–2)
Then/Now
New Vocabulary
Key Concept: Distance Formula (on Number Line)
Example 1: Find Distance on a Number Line
Key Concept: Distance Formula (in Coordinate Plane)
Example 2: Find Distance on Coordinate Plane
Key Concept: Midpoint Formula (on Number Line)
Example 3: Real-World Example: Find Midpoint on Number Line
Key Concept: Midpoint Formula (in Coordinate Plane)
Example 4: Find Midpoint in Coordinate Plane
Example 5: Find the Coordinates of an Endpoint
Example 6: Use Algebra to Find Measures
Over Lesson 1–2
What is the value of x and AB if B is between A and
C, AB = 3x + 2, BC = 7, and AB = 8x – 1?
A. x = 2, AB = 8
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B
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A
D. x = –2, AB = –4
A
B
C
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D
D
C.
A.
B.
C.
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D.
C
B. x = 1, AB = 5
Over Lesson 1–2
If M is between L and N, LN = 3x – 1, LM = 4, and
MN = x – 1, what is the value of x and MN?
A. x = 1, MN = 0
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B
A
D. x = 4, MN = 3
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A
B
C
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D
D
C. x = 3, MN = 2
A.
B.
C.
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D.
C
B. x = 2, MN = 1
Over Lesson 1–2
Find RT.
C.
.
D.
in.
0%
0%
A.
B.
C.
0%
D.
A
B
C
0%
D
D
in.
C
B.
B
.
A
A.
Over Lesson 1–2
What segment is congruent
to MN?
A. MQ
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B
A
D. no congruent segments
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A
B
C
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D
D
C. NQ
A.
B.
C.
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D.
C
B. QN
Over Lesson 1–2
What segment is congruent
to NQ?
A. MN
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B
A
D. no congruent segments
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A
B
C
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D
D
C. QM
A.
B.
C.
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D.
C
B. NM
Over Lesson 1–2
A. 5
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B
D. 18
A
0%
A
B
C
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D
D
C. 14
C
B. 6
A.
B.
C.
0%
D.
You graphed points on the coordinate plane.
(Lesson 0–2)
• Find the distance between two points.
• Find the midpoint of a segment.
• distance
• midpoint
• segment bisector
Find Distance on a Number Line
Use the number line to find QR.
The coordinates of Q and R are –6 and –3.
QR = | –6 – (–3) |
= | –3 | or 3
Answer: 3
Distance Formula
Simplify.
Use the number line to find AX.
A. 2
B. 8
0%
B
A
0%
A
B
C
0%
D
D
D. –8
C
C. –2
A.
B.
C.
0%
D.
Find Distance on a Coordinate Plane
Find the distance between E(–4, 1) and F(3, –1).
(x1, y1) = (–4, 1) and
(x2, y2) = (3, –1)
Find Distance on a Coordinate Plane
Check Graph the ordered pairs
and check by using the
Pythagorean Theorem.
Find Distance on a Coordinate Plane
.
Find the distance between A(–3, 4) and M(1, 2).
A. 4
B.
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B
A
0%
A
B
C
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D
D
D.
A.
B.
C.
0%
D.
C
C.
Find Midpoint on a Number Line
DECORATING Marco places a couch so that its end
is perpendicular and 2.5 feet away from the wall.
The couch is 90” wide. How far is the midpoint of
the couch back from the wall in feet?
First we must convert 90 inches to 7.5 feet. The
coordinates of the endpoints of the couch are 2.5 and
10. Let M be the midpoint of the couch.
Midpoint Formula
x1 = 2.5, x2 = 10
Find Midpoint on a Number Line
Simplify.
Answer: The midpoint of the couch back is 6.25 feet
from the wall.
DRAG RACING The length of a drag racing strip is
mile long. How many feet from the finish line is
the midpoint of the racing strip?
A. 330 ft
0%
B
D. 1320 ft
A
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A
B
C
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D
D
C. 990 ft
C
B. 660 ft
A.
B.
C.
0%
D.
Find Midpoint in Coordinate Plane
Answer: (–3, 3)
A. (–10, –6)
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B
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A
D. (–6, –12)
A
B
C
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D
D
C. (6, 12)
A.
B.
C.
0%
D.
C
B. (–5, –3)
Find the Coordinates of an Endpoint
Let D be (x1, y1) and F be (x2, y2) in the Midpoint
Formula.
(x2, y2) =
Write two equations to find the coordinates of D.
Find the Coordinates of an Endpoint
Midpoint Formula
Midpoint Formula
Answer: The coordinates of D are (–7, 11).
Find the coordinates of R if N (8, –3) is the midpoint
of RS and S has coordinates (–1, 5).
A. (3.5, 1)
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B
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A
D. (17, –11)
A
B
C
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D
D
C. (15, –1)
A.
B.
C.
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D.
C
B. (–10, 13)
Use Algebra to Find Measures
Understand
You know that Q is the midpoint of PR,
and the figure gives algebraic measures
for QR and PR. You are asked to find
the measure of PR.
Use Algebra to Find Measures
Plan
Because Q is the midpoint, you know
that
Use this equation and the algebraic measures to find a
value for x.
Solve
Subtract 1 from each side.
Use Algebra to Find Measures
Original measure
Use Algebra to Find Measures
Check
QR = 6 – 3x
Original Measure
Use Algebra to Find Measures
Multiply.
Simplify.
A. 1
B. 3
D. 10
0%
B
A
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0%
C
C. 5
A
B
C
D
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D
A.
B.
C.
D.