applying the pythagorean theorem and its converse
find the length of each side of the triangle. simplify and write your answer in the form sqrt(__) with no spaces.
ab =
ac =

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{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem" ], "new_concepts": [ "Distance Formula on Coordinate Plane" ], "current_concepts": [ "Pythagorean Theorem", "Distance Formula on Coordinate Plane" ] } ## Identify coordinates of the vertices $$ A = (-2, 1),\quad B = (8, -3),\quad C = (2, 4) $$ ## Calculate the length of AB $$ \begin{aligned} AB &= \sqrt{(8 - (-2))^2 + (-3 - 1)^2} \ &= \sqrt{10^2 + (-4)^2} \ &= \sqrt{100 + 16} \ &= \sqrt{116} \end{aligned} $$ ## Calculate the length of AC $$ \begin{aligned} AC &= \sqrt{(2 - (-2))^2 + (4 - 1)^2} \ &= \sqrt{4^2 + 3^2} \ &= \sqrt{16 + 9} \ &= \sqrt{25} \end{aligned} $$ ## Question 1 AB = sqrt(116) ## Question 2 AC = sqrt(25) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula on Coordinate Plane" ] }

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Explanation:

Identify coordinates of the vertices

Calculate the length of AB

Calculate the length of AC

Answer:

Question 1

Question 2