Mathematics
Grade 10
15 min
Lengths of segments on number lines: Set 2
Lengths of segments on number lines: Set 2
What you'll learn
- Solve addition problems involving money amounts (dollars and cents) with at least 80% accuracy.
- Solve subtraction problems involving money amounts (dollars and cents) with at least 80% accuracy.
- Explain the steps to add or subtract money amounts, including how to regroup when necessary, in their own words.
- Apply addition and subtraction of money amounts to solve one-step word problems related to real-life scenarios like buying items at a store.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the length of a segment on a number line when coordinates are given as algebraic expressions.
Apply the Segment Addition Postulate to solve for unknown variables and segment lengths.
Determine the coordinate of a point that partitions a segment on a number line into a given ratio.
Use the definition of a midpoint to find the coordinates of endpoints or midpoints.
Prove that two segments on a number line are congruent by calculating and comparing their lengths.
Solve multi-step problems involving segment bisectors and algebraic expressions.
Interpret absolute value as the distance between two points on a number line in formal proofs.
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2
Key Concepts & Vocabulary
TermDefinitionExample
Segment Addition PostulateIf three points A, B, and C are collinear and B is between A and C, then the length of segment AB plus the length of segment BC is equal to the length of the entire segment AC.If point A is at -2, B is at 3, and C is at 10, then AB = 5 and BC = 7. The postulate states AB + BC = AC, so 5 + 7 = 12. The length of AC is indeed |10 - (-2)| = 12.
Midpoint of a SegmentA point that divides a segment into two congruent (equal length) segments.If M is the midpoint of segment PQ, where P is at 2 and Q is at 10, then M is at coordinate 6. The length PM = 4 and MQ = 4.
Segment BisectorA point, line, ray, or another segment that intersects a segment at its midpoint, thus dividing it into two equal parts.If line *l* intersects segment AB at its midpoint M,...
3
Core Formulas
Distance Formula on a Number Line
d = |x₂ - x₁|
To find the length of a segment, take the absolute value of the difference between the coordinates of its endpoints, x₁ and x₂. This ensures the distance is always a non-negative value.
Midpoint Formula on a Number Line
M = (x₁ + x₂)/2
To find the coordinate of the midpoint (M) of a segment, add the coordinates of the endpoints (x₁ and x₂) and divide by 2. This is the average of the coordinates.
Segment Partition Formula (1D)
P = x₁ + (m/(m+n))(x₂ - x₁)
To find the coordinate of a point P that divides the directed segment from x₁ to x₂ in the ratio m:n, you add a fraction of the total segment length to the starting coordinate.
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Challenging
Point M is the midpoint of segment AB. The coordinate of A is given by x-1, the coordinate of M is 3x+1, and the coordinate of B is 8x. Find the coordinate of endpoint B.
A.1
B.4
C.7
D.8
Challenging
On a number line, S is the midpoint of RT. R is the midpoint of PS. If the coordinate of S is 10 and the coordinate of T is 14, what is the coordinate of P?
A.12
B.8
C.2
D.6
Challenging
Point P partitions the directed segment AB from A at coordinate x to B at coordinate 5x. If the coordinate of P is 16 and the ratio of AP to PB is 3:1, what is the value of x?
A.4
B.3
C.2
D.1
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What grade level is "Lengths of segments on number lines: Set 2"?
Lengths of segments on number lines: Set 2 is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Lengths of segments on number lines: Set 2?
You'll be able to: Solve addition problems involving money amounts (dollars and cents) with at least 80% accuracy; Solve subtraction problems involving money amounts (dollars and cents) with at least 80% accuracy; Explain the steps to add or….
Is "Lengths of segments on number lines: Set 2" free to practice?
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How many practice questions are included with Lengths of segments on number lines: Set 2?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.