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Five-Minute Check (over Lesson 1–2)
NGSSS
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
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
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
B. x = 1, AB = 5
C.
D. x = –2, AB = –4
Over Lesson 1–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. x = 1, MN = 0
B. x = 2, MN = 1
C. x = 3, MN = 2
D. x = 4, MN = 3
If M is between L and N, LN = 3x – 1, LM = 4, and MN = x – 1, what is the value of x and MN?
Over Lesson 1–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Find RT.
A.
B.
C.
D.
.
.
in.
in.
Over Lesson 1–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
What segment is congruent to MN?
A. MQ
B. QN
C. NQ
D. no congruent segments
Over Lesson 1–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
What segment is congruent to NQ?
A. MN
B. NM
C. QM
D. no congruent segments
Over Lesson 1–2
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 5
B. 6
C. 14
D. 18
MA.912.G.1.1 Find the lengths and midpoints of line segments in two-dimensional coordinate systems.
MA.912.G.1.2 Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass or a drawing program, explaining and justifying the process used.
You graphed points on the coordinate plane. (Lesson 0–2)
• Find the distance between two points.
• Find the midpoint of a segment.
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) | Distance Formula
= | –3 | or 3 Simplify.
Answer: 3
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 2
B. 8
C. –2
D. –8
Use the number line to find AX.
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
.
A. 4
B.
C.
D.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Find the distance between A(–3, 4) and M(1, 2).
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.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 330 ft
B. 660 ft
C. 990 ft
D. 1320 ft
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?
Find Midpoint in Coordinate Plane
Answer: (–3, 3)
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. (–10, –6)
B. (–5, –3)
C. (6, 12)
D. (–6, –12)
Find the Coordinates of an Endpoint
Write two equations to find the coordinates of D.
Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula.
Find the Coordinates of an Endpoint
Answer: The coordinates of D are (–7, 11).
Midpoint Formula
Midpoint Formula
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. (3.5, 1)
B. (–10, 13)
C. (15, –1)
D. (17, –11)
Find the coordinates of R if N (8, –3) is the midpointof RS and S has coordinates (–1, 5).
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
Use this equation and the algebraic measures to find a value for x.
Plan Because Q is the midpoint, you know
that
Solve
Subtract 1 from each side.
Original measure
Use Algebra to Find Measures
Use Algebra to Find Measures
Check
QR = 6 – 3x Original Measure
Use Algebra to Find Measures
Multiply.
Simplify.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 1
B. 3
C. 5
D. 10
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