{"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":"f915e265-3b32-5fa0-8fdf-0ffb9a732222","task_key":"precalculus--test--f915e265-3b32-5fa0-8fdf-0ffb9a732222","task_revision_id":"1","upstream_id":"","short_description":"Let $x_1,$ $x_2,$ $x_3,$ $y_1,$ $y_2,$ and $y_3$ be real numbers such that","config":"precalculus","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Let $x_1,$ $x_2,$ $x_3,$ $y_1,$ $y_2,$ and $y_3$ be real numbers such that\\n\\\\begin{align*}\\n(x_1 - x_2)^2 + (y_1 - y_2)^2 &= 9, \\\\\\\\\\n(x_1 - x_3)^2 + (y_1 - y_3)^2 &= 16, \\\\\\\\\\n(x_2 - x_3)^2 + (y_2 - y_3)^2 &= 25.\\n\\\\end{align*}Find $\\\\begin{vmatrix} x_1 & y_1 & 1 \\\\\\\\ x_2 & y_2 & 1 \\\\\\\\ x_3 & y_3 & 1 \\\\end{vmatrix}^2.$\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}