{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"9884307e-1431-57e6-87e2-bc54d0e40b93","task_key":"geometry--test--9884307e-1431-57e6-87e2-bc54d0e40b93","task_revision_id":"1","upstream_id":"","short_description":"The lines $y = -2x + 8$ and $y = \\frac{1}{2} x - 2$ meet at $(4,0),$ as shown.…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The lines $y = -2x + 8$ and $y = \\\\frac{1}{2} x - 2$ meet at $(4,0),$ as shown. What is the area of the triangle formed by these two lines and the line $x = -2?$ [asy]\\ndraw((-8,0)--(15,0),black+linewidth(1));\\ndraw((-8,0)--(15,0),EndArrow);\\ndraw((0,-8)--(0,15),black+linewidth(1));\\ndraw((0,-8)--(0,15),EndArrow);\\ndraw((-2,-9)--(-2,16),black+linewidth(1));\\ndraw((-3.5,15)--(8,-8),black+linewidth(1));\\ndraw((-8,-6)--(8,2),black+linewidth(1));\\nlabel(\\\"$y$\\\",(0,15),N);\\nlabel(\\\"$x$\\\",(15,0),E);\\nlabel(\\\"$x=-2$\\\",(-2,-9),S);\\nlabel(\\\"$(4,0)$\\\",(3,-2),S);\\nlabel(\\\"$y=\\\\frac{1}{2}x-2$\\\",(8,2),NE);\\nlabel(\\\"$y=-2x+8$\\\",(8,-8),SE);\\n[/asy]\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}