lesson 4 - 1
1. if q is between a and m and mq = 7.3 and am = 8.5, then qa =?
a. 5.8 b. 1.2 c. 7.3 d. 14.6
2. given: k is between h and j, hk = 2x - 5, kj = 3x + 4, and hj = 24. what is the value of x?
a. 9 b. 5 c. 19 d. 3
3. if k is the mid - point of (overline{hj}), hk = x + 6, and hj = 4x - 6, then kj =?
a. 15 b. 9 c. 4 d. 10
4. state the segment addition postulate in your own words.
5. explain what distance along a line means as an undefined term in geometry.

Question

Accepted Answer

# Explanation:
## Step1: Use segment - addition property
Since $Q$ is between $A$ and $M$, we know that $AM=QA + MQ$. We are given $MQ = 7.3$ and $AM = 8.5$. Then $QA=AM - MQ$.
## Step2: Substitute values
Substitute $AM = 8.5$ and $MQ = 7.3$ into the formula $QA=AM - MQ$, we get $QA=8.5 - 7.3=1.2$.
# Answer:
B. 1.2

# Explanation:
## Step1: Apply segment - addition postulate
Since $K$ is between $H$ and $J$, $HJ=HK + KJ$. Given $HK = 2x-5$, $KJ = 3x + 4$, and $HJ = 24$, we substitute these values into the equation: $24=(2x - 5)+(3x + 4)$.
## Step2: Simplify the equation
First, combine like - terms: $24=2x-5 + 3x + 4=5x-1$.
## Step3: Solve for $x$
Add 1 to both sides of the equation: $24 + 1=5x$, so $25 = 5x$. Then divide both sides by 5, $x = 5$.
# Answer:
B. 5

# Explanation:
## Step1: Use mid - point property
If $K$ is the mid - point of $\overline{HJ}$, then $HK=KJ$ and $HJ = 2HK$. Given $HK=x + 6$ and $HJ = 4x-6$, and since $HJ = 2HK$, we have $4x-6=2(x + 6)$.
## Step2: Expand and solve for $x$
Expand the right - hand side: $4x-6=2x+12$. Subtract $2x$ from both sides: $4x-2x-6=2x-2x + 12$, which gives $2x-6=12$. Add 6 to both sides: $2x=12 + 6=18$, so $x = 9$.
## Step3: Find $KJ$
Since $KJ=HK=x + 6$, substitute $x = 9$ into $HK$, then $KJ=9 + 6=15$.
# Answer:
A. 15

# Brief Explanations:
The Segment Addition Postulate states that if we have three points $A$, $B$, and $C$ that are collinear (lying on the same line) and $B$ is between $A$ and $C$, then the length of segment $AC$ is equal to the sum of the lengths of segments $AB$ and $BC$, i.e., $AC=AB + BC$.
# Answer:
If three points are collinear and one is between the other two, the length of the whole segment is the sum of the lengths of the two sub - segments.

# Brief Explanations:
In geometry, the distance along a line (as an undefined term) refers to the non - negative amount of space between two points on that line. It is a fundamental concept that we use to measure how far apart two points are on a straight path. We can think of it as the shortest path between two points on the line and it is always a non - negative value.
# Answer:
The non - negative amount of space between two points on a line, a fundamental measure of separation on a straight path.

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QUESTION IMAGE

Question

Explanation:

Step1: Use segment - addition property

Step2: Substitute values

Step1: Apply segment - addition postulate

Step2: Simplify the equation

Step3: Solve for \(x\)

Step1: Use mid - point property

Step2: Expand and solve for \(x\)

Step3: Find \(KJ\)

Answer: