{ "query": { "display": "midpoint $$\\left(8,\\:-10\\right),\\:\\left(-10,\\:-8\\right)$$", "symbolab_question": "PRE_CALC#midpoint (8,-10),(-10,-8)" }, "solution": { "level": "PERFORMED", "subject": "Functions & Graphing", "topic": "Line Equations", "subTopic": "Midpoint", "default": "(-1,-9)", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Midpoint of$$\\left(8,\\:-10\\right)$$ and $$\\left(-10,\\:-8\\right):{\\quad}\\left(-1,\\:-9\\right)$$", "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": [ "$$\\left(x_1,\\:y_1\\right)=\\left(8,\\:-10\\right),\\:\\left(x_2,\\:y_2\\right)=\\left(-10,\\:-8\\right)$$" ], "result": "=\\left(\\frac{-10+8}{2},\\:\\frac{-8-10}{2}\\right)" }, { "type": "step", "primary": "Refine", "result": "=\\left(-1,\\:-9\\right)" } ], "meta": { "solvingClass": "PreCalc" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "pointsToDraw": { "pointsLatex": [ "(-1,-9)", "(8,-10)", "(-10,-8)" ], "pointsDecimal": [ { "fst": -1, "snd": -9 }, { "fst": 8, "snd": -10 }, { "fst": -10, "snd": -8 } ], "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": "(8,-10), (-1,-9), (-10,-8)", "paramsLatex": [], "paramsReplacementsLatex": [] } ], "localBoundingBox": { "xMin": -22.599999999999998, "xMax": 20.599999999999998, "yMin": -17.77, "yMax": 8.869999999999997 } }, "showViewLarger": true } }, "meta": { "showVerify": true } }