for any answers with a square root, write your answer in the form sqrt(____) with no spaces.

find the length of each segment.

$fe =$
$ed =$
$fd =$

Question

for any answers with a square root, write your answer in the form sqrt(____) with no spaces.

find the length of each segment.

$fe =$
$ed =$
$fd =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Coordinate Geometry" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Coordinate Geometry" ] } ## Identify coordinates of the vertices Using the **Coordinate Geometry** knowledge point $$ \begin{aligned} &D = (-1, 0)\ &E = (-3, 4)\ &F = (-5, 4) \end{aligned} $$ ## Calculate the length of segment FE Using the **Coordinate Geometry** knowledge point $$ \begin{aligned} &FE = \sqrt{(-3 - (-5))^2 + (4 - 4)^2}\ &FE = \sqrt{2^2 + 0^2} = 2 \end{aligned} $$ ## Calculate the length of segment ED Using the *Distance Formula* knowledge point $$ \begin{aligned} &ED = \sqrt{(-1 - (-3))^2 + (0 - 4)^2}\ &ED = \sqrt{2^2 + (-4)^2} = \sqrt{4 + 16} = \sqrt{20} \end{aligned} $$ ## Calculate the length of segment FD Using the *Distance Formula* knowledge point $$ \begin{aligned} &FD = \sqrt{(-1 - (-5))^2 + (0 - 4)^2}\ &FD = \sqrt{4^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} \end{aligned} $$ Find the length of each segment. $FE =$ 2 $ED =$ sqrt(20) $FD =$ sqrt(32) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of the vertices

Calculate the length of segment FE

Calculate the length of segment ED

Calculate the length of segment FD

Answer: