{ "query": { "display": "midpoint $$\\left(-2,\\:-7\\right),\\:\\left(7,\\:4\\right)$$", "symbolab_question": "PRE_CALC#midpoint (-2,-7),(7,4)" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Midpoint", "default": "(\\frac{5}{2},-\\frac{3}{2})", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Midpoint of$$\\left(-2,\\:-7\\right)$$ and $$\\left(7,\\:4\\right):{\\quad}\\left(\\frac{5}{2},\\:-\\frac{3}{2}\\right)$$", "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": [ "$$\\left(x_1,\\:y_1\\right)=\\left(-2,\\:-7\\right),\\:\\left(x_2,\\:y_2\\right)=\\left(7,\\:4\\right)$$" ], "result": "=\\left(\\frac{7-2}{2},\\:\\frac{4-7}{2}\\right)" }, { "type": "step", "primary": "Refine", "result": "=\\left(\\frac{5}{2},\\:-\\frac{3}{2}\\right)" } ], "meta": { "solvingClass": "PreCalc" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "pointsToDraw": { "pointsLatex": [ "(\\frac{5}{2},-\\frac{3}{2})", "(-2,-7)", "(7,4)" ], "pointsDecimal": [ { "fst": 2.5, "snd": -1.5 }, { "fst": -2, "snd": -7 }, { "fst": 7, "snd": 4 } ], "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": "(-2,-7), (\\frac{5}{2},-\\frac{3}{2}), (7,4)", "paramsLatex": [], "paramsReplacementsLatex": [] } ], "localBoundingBox": { "xMin": -8.299999999999999, "xMax": 13.299999999999999, "yMin": -14.7, "yMax": 11.7 } }, "showViewLarger": true } }, "meta": { "showVerify": true } }