{"id":"cb_question_bank:c310a794-e5e8-4019-9049-8c18f4d67fb9","source_id":"cb_question_bank","source_item_id":"c310a794-e5e8-4019-9049-8c18f4d67fb9","external_id":"8f07857d-c0af-4793-9305-0e414671d257","ibn":null,"question_id":"eb70d2d0","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Moving from left to right, the points have the following coordinates: (negative 3 comma 4) (4 comma negative 3) (5 comma 3) What is the area, in square units, of the triangle formed by connecting the three points shown?","stimulus":"","stimulus_html":null,"stem_html":"

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

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What is the area, in square units, of the triangle formed by connecting the three points shown?

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The correct answer is 24.5. It's given that a triangle is formed by connecting the three points shown, which are -3,4, 5,3, and 4,-3. Let this triangle be triangle A. The area of triangle A can be found by calculating the area of the rectangle that circumscribes it and subtracting the areas of the three triangles that are inside the rectangle but outside triangle A. The rectangle formed by the points -3,4, 5,4, 5,-3, and -3,-3 circumscribes triangle A. The width, in units, of this rectangle can be found by calculating the distance between the points 5,4 and 5,-3. This distance is 4--3, or 7\n. The length, in units, of this rectangle can be found by calculating the distance between the points 5,4 and -3,4. This distance is 5--3, or 8\n. It follows that the area, in square units, of the rectangle is 78, or 56\n. One of the triangles that lies inside the rectangle but outside triangle A is formed by the points -3,4, 5,4, and 5,3. The length, in units, of a base of this triangle can be found by calculating the distance between the points 5,4 and 5,3. This distance is 4-3, or 1\n. The corresponding height, in units, of this triangle can be found by calculating the distance between the points 5,4 and -3,4. This distance is 5--3, or 8\n. It follows that the area, in square units, of this triangle is 1281, or 4\n. A second triangle that lies inside the rectangle but outside triangle A is formed by the points 4,-3, 5,3, and 5,-3. The length, in units, of a base of this triangle can be found by calculating the distance between the points 5,3 and 5,-3. This distance is 3--3 , or 6\n. The corresponding height, in units, of this triangle can be found by calculating the distance between the points 5,-3 and 4,-3. This distance is 5-4, or 1\n. It follows that the area, in square units, of this triangle is 1216, or 3\n. The third triangle that lies inside the rectangle but outside triangle A is formed by the points -3,4, -3,-3, and 4,-3. The length, in units, of a base of this triangle can be found by calculating the distance between the points 4,-3 and -3,-3. This distance is 4--3, or 7\n. The corresponding height, in units, of this triangle can be found by calculating the distance between the points -3,4 and -3,-3. This distance is 4--3, or 7\n. It follows that the area, in square units, of this triangle is 1277, or 24.5. Thus, the area, in square units, of the triangle formed by connecting the three points shown is 56-4-3-24.5, or 24.5. Note that 24.5 and 49/2 are examples of ways to enter a correct answer.

","correct_answer":["24.5","49/2"],"has_media":true,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.836000+00:00","source_updated_at":"2023-08-02T20:25:59.836000+00:00","options":[],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}