{ "query": { "display": "midpoint $$\\left(3.2,\\:2.5\\right),\\:\\left(1.6,\\:-4.5\\right)$$", "symbolab_question": "PRE_CALC#midpoint (3.2,2.5),(1.6,-4.5)" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Midpoint", "default": "(2.4,-1)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Midpoint of$$\\left(3.2,\\:2.5\\right)$$ and $$\\left(1.6,\\:-4.5\\right):{\\quad}\\left(2.4,\\:-1\\right)$$", "steps": [ { "type": "step", "primary": "Midpoint of $$\\left(x_1,\\:y_1\\right),\\:\\left(x_2,\\:y_2\\right)$$: $$\\left(\\frac{x_2+x_1}{2},\\:\\:\\frac{y_2+y_1}{2}\\right)$$", "secondary": [ "$$\\left(x_1,\\:y_1\\right)=\\left(3.2,\\:2.5\\right),\\:\\left(x_2,\\:y_2\\right)=\\left(1.6,\\:-4.5\\right)$$" ], "result": "=\\left(\\frac{1.6+3.2}{2},\\:\\frac{-4.5+2.5}{2}\\right)" }, { "type": "step", "primary": "Refine", "result": "=\\left(2.4,\\:-1\\right)" } ], "meta": { "solvingClass": "PreCalc" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "pointsToDraw": { "pointsLatex": [ "(2.4,-1)", "(3.2,2.5)", "(1.6,-4.5)" ], "pointsDecimal": [ { "fst": 2.4, "snd": -1 }, { "fst": 3.2, "snd": 2.5 }, { "fst": 1.6, "snd": -4.5 } ], "attributes": [ { "color": "BLACK", "labels": [ "\\mathrm{Mid\\:Point}" ], "labelTypes": [ "SOLUTION" ], "labelColors": [ "BLACK" ] }, { "color": "PURPLE", "labels": [ "\\mathrm{First\\:Point}" ], "labelTypes": [ "DEFAULT" ], "labelColors": [ "PURPLE" ] }, { "color": "PURPLE", "labels": [ "\\mathrm{Second\\:Point}" ], "labelTypes": [ "DEFAULT" ], "labelColors": [ "PURPLE" ] } ] }, "functionChanges": [ { "origFormulaLatex": [], "finalFormulaLatex": [], "plotTitle": "(3.2,2.5), (2.4,-1), (1.6,-4.5)", "paramsLatex": [], "paramsReplacementsLatex": [] } ], "localBoundingBox": { "xMin": -2.784, "xMax": 5.664000000000001, "yMin": -9.4, "yMax": 7.4 } }, "showViewLarger": true } }, "meta": { "showVerify": true } }