what point on the number line is $\frac{1}{4}$ of the way from the point 0 to the point $-3$?

$-0.25$
$-0.5$
$-0.75$
$-1$

Question

what point on the number line is $\frac{1}{4}$ of the way from the point 0 to the point $-3$?

$-0.25$
$-0.5$
$-0.75$
$-1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Segment Length Ratio" ], "new_concepts": [ "Number Line Partitioning" ], "current_concepts": [ "Segment Length Ratio", "Number Line Partitioning" ] } ## Identify the given values and target Using the *Segment Length Ratio* knowledge point $$ \begin{aligned} &\text{Start point } (A) = 0\ &\text{End point } (B) = -3\ &\text{Fractional distance } (k) = \frac{1}{4} \end{aligned} $$ ## Calculate the partitioned coordinate Using the *Segment Length Ratio* knowledge point $$ \begin{aligned} P &= A + k(B - A)\ P &= 0 + \frac{1}{4}(-3 - 0)\ P &= -\frac{3}{4} = -0.75 \end{aligned} $$

(A) $-0.25$

(B) $-0.5$

(C) $-0.75$

(D) $-1$

{ "elements": [ { "type": "line", "params": [[-4, 0], [1, 0]], "properties": { "strokeColor": "#583C87", "strokeWidth": 2 } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "0", "color": "#8C55F2", "size": 4, "withLabel": true } }, { "type": "point", "params": [[-3, 0]], "properties": { "name": "-3", "color": "#8C55F2", "size": 4, "withLabel": true } }, { "type": "point", "params": [[-0.75, 0]], "properties": { "name": "-0.75", "color": "#F2557F", "size": 5, "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Segment Length Ratio" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the given values and target

Calculate the partitioned coordinate

Answer: