which value of $x$ would make $\overline{no} \parallel \overline{kj}$?

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Question

which value of $x$ would make $\overline{no} \parallel \overline{kj}$?

$\bigcirc$ 1
$\bigcirc$ 6
$\bigcirc$ 8
$\bigcirc$ 10

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [ "Triangle Proportionality Theorem" ], "new_concepts": [], "current_concepts": [ "Triangle Proportionality Theorem", "Triangle Geometry" ] } ## Set up the proportionality equation Using the **Triangle Proportionality Theorem** $$ \frac{KN}{NL} = \frac{JO}{OL} $$ $$ \frac{x + 2}{x - 3} = \frac{x}{x - 4} $$ ## Solve the rational equation Using the **Triangle Proportionality Theorem** $$ \begin{aligned} (x + 2)(x - 4) &= x(x - 3) \ x^2 - 2x - 8 &= x^2 - 3x \ -2x - 8 &= -3x \ x &= 8 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Proportionality Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the proportionality equation

Solve the rational equation

Answer: