{"id":"aqua_rat:6de97049af40c8b82b6283a3a6cbb2b6","source_id":"aqua_rat","source_item_id":"6de97049af40c8b82b6283a3a6cbb2b6","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"In the coordinate plane, a triangle has vertices at (a,0), (b,0), and (x,y). If a>x>b>0>y, which of the following represents the area of that triangle?","stimulus":"","stimulus_html":null,"stem_html":"<p>In the coordinate plane, a triangle has vertices at (a,0), (b,0), and (x,y). If a&gt;x&gt;b&gt;0&gt;y, which of the following represents the area of that triangle?</p>","rationale_html":"<p>We must plug in the three points that satisfy y&lt;0&lt;b&lt;x&lt;a.</p><p>Only C satisfies the area of a triangle.</p><p>C. (by−ay)/2</p>","correct_answer":["C"],"equiv_key":"898889dac1e4a95e588d41a6","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>(ay−by)/2</p>","ord":0},{"label":"B","content_html":"<p>(ab−ay)/2</p>","ord":1},{"label":"C","content_html":"<p>(by−ay)/2</p>","ord":2},{"label":"D","content_html":"<p>(ay+by)/x</p>","ord":3},{"label":"E","content_html":"<p>(a−b)/2y</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}