question 13 (1 point)
the points a(0, 0), b(2, 3), and c(4, 0) are the vertices of a triangle. identify the type of triangle abc is.
obtuse
equilateral
right isosceles
isosceles

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Coordinate Geometry", "Distance Formula" ], "new_concepts": [ "Triangle Classification" ], "current_concepts": [ "Coordinate Geometry", "Distance Formula", "Triangle Classification" ] } ## Calculate the lengths of the three sides Using the **Distance Formula** in **Coordinate Geometry**: $$ \begin{aligned} AB &= \sqrt{(2-0)^2 + (3-0)^2} = \sqrt{4 + 9} = \sqrt{13} \ BC &= \sqrt{(4-2)^2 + (0-3)^2} = \sqrt{4 + 9} = \sqrt{13} \ AC &= \sqrt{(4-0)^2 + (0-0)^2} = \sqrt{16 + 0} = 4 \end{aligned} $$ ## Classify the triangle based on side lengths Comparing the calculated side lengths: $$ \begin{aligned} &AB = BC = \sqrt{13} eq AC \ &(\sqrt{13})^2 + (\sqrt{13})^2 = 13 + 13 = 26 eq 4^2 \end{aligned} $$ Since two sides are equal, the triangle is isosceles but not right-angled or equilateral.

obtuse

equilateral

right isosceles

isosceles

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Question

Explanation:

Calculate the lengths of the three sides

Classify the triangle based on side lengths

Answer: