square efgh is drawn on a coordinate plane. side fe is on the line $y - 2 = -2(x + 6)$. what is the slope of the side fg?

* $-\frac{1}{2}$
* $\frac{1}{2}$
* $-2$
* $2$

Question

square efgh is drawn on a coordinate plane. side fe is on the line $y - 2 = -2(x + 6)$. what is the slope of the side fg?

* $-\frac{1}{2}$
* $\frac{1}{2}$
* $-2$
* $2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Lines", "Slope Formula" ], "new_concepts": [ "Properties of Squares" ], "current_concepts": [ "Perpendicular Lines", "Slope Formula", "Properties of Squares" ] } ## Identify the slope of the line containing side FE $$ \begin{aligned} &y - 2 = -2(x + 6) \ &m_{FE} = -2 \end{aligned} $$ ## Determine the relationship between adjacent sides of a square $$ \begin{aligned} &FE \perp FG \ &m_{FG} = -\frac{1}{m_{FE}} \end{aligned} $$ ## Calculate the slope of side FG $$ \begin{aligned} &m_{FG} = -\frac{1}{-2} = \frac{1}{2} \end{aligned} $$

(A) $-\frac{1}{2}$

(B) $\frac{1}{2}$

(C) $-2$

(D) $2$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Lines" ] }

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Question

Explanation:

Identify the slope of the line containing side FE

Determine the relationship between adjacent sides of a square

Calculate the slope of side FG

Answer: