practice exercises

find the distance between the two points.
1. $-2$ and $8$
2. $12$ and $4$
3. $-5$ and $-9$
4. $-7$ and $15$

5. name the points on the line whose distance is $2$ units from point $g$.
6. name the points on the line whose distance is $3$ units from point $d$.
7. name the points on the line whose distance is $5$ units from point $f$.

find the value of $x$.
8.
9.
10. $m$ is the midpoint of $\overline{bc}$.
11. $m$ is the midpoint of $\overline{ef}$.

Question

practice exercises

find the distance between the two points.
1. $-2$ and $8$
2. $12$ and $4$
3. $-5$ and $-9$
4. $-7$ and $15$

5. name the points on the line whose distance is $2$ units from point $g$.
6. name the points on the line whose distance is $3$ units from point $d$.
7. name the points on the line whose distance is $5$ units from point $f$.

find the value of $x$.
8.
9.
10. $m$ is the midpoint of $\overline{bc}$.
11. $m$ is the midpoint of $\overline{ef}$.

Accepted Answer

{ "quality": "clear", "question_count": 11, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Distance on Number Line", "Segment Addition Postulate", "Midpoint Definition" ], "current_concepts": [ "Distance on Number Line", "Segment Addition Postulate", "Midpoint Definition" ] } ## Calculate distances on a number line (Questions 1-4) $$ \begin{aligned} &\text{Q1: } |-2 - 8| = |-10| = 10\ &\text{Q2: } |12 - 4| = |8| = 8\ &\text{Q3: } |-5 - (-9)| = |-5 + 9| = 4\ &\text{Q4: } |-7 - 15| = |-22| = 22 \end{aligned} $$ ## Find points at a given distance (Questions 5-7) $$ \begin{aligned} &\text{Q5: } G = 1. \text{ Points at distance 2: } 1 - 2 = -1 \ (E), \ 1 + 2 = 3 \ (I)\ &\text{Q6: } D = -2. \text{ Points at distance 3: } -2 - 3 = -5 \ (A), \ -2 + 3 = 1 \ (G)\ &\text{Q7: } F = 0. \text{ Points at distance 5: } 0 - 5 = -5 \ (A), \ 0 + 5 = 5 \ (K) \end{aligned} $$ ## Solve for x using segment properties (Questions 8-11) $$ \begin{aligned} &\text{Q8: } 5x + 11 = 41 \implies 5x = 30 \implies x = 6\ &\text{Q9: } 26 = 12 - 7x \implies 7x = -14 \implies x = -2\ &\text{Q10: } M \text{ is midpoint of } BC \implies BC = 2 \cdot BM \implies 36 = 2(6x) \implies 12x = 36 \implies x = 3\ &\text{Q11: } M \text{ is midpoint of } EF \implies EF = 2 \cdot MF \implies 24 = 2(4x) \implies 8x = 24 \implies x = 3 \end{aligned} $$ | No. | Answer | |---|---| | 1 | $10$ | | 2 | $8$ | | 3 | $4$ | | 4 | $22$ | | 5 | $E$ and $I$ | | 6 | $A$ and $G$ | | 7 | $A$ and $K$ | | 8 | $x = 6$ | | 9 | $x = -2$ | | 10 | $x = 3$ | | 11 | $x = 3$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Segment Addition Postulate" ] }

No.	Answer
2	\(8\)
3	\(4\)
4	\(22\)
5	\(E\) and \(I\)
6	\(A\) and \(G\)
7	\(A\) and \(K\)
8	\(x = 6\)
9	\(x = -2\)
10	\(x = 3\)
11	\(x = 3\)

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QUESTION IMAGE

Question

Explanation:

Calculate distances on a number line (Questions 1-4)

Find points at a given distance (Questions 5-7)

Solve for x using segment properties (Questions 8-11)

Answer: