Calculate the distance between two points.
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"}, "dy": {"definition": "ya2-ya1", "name": "dy", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "xa1": {"definition": "l[0]", "name": "xa1", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "y2": {"definition": "y1+random([-1,1])*triple[1]", "name": "y2", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "extensions": ["jsxgraph"], "rulesets": {}, "name": "Katherine's copy of Distance between two points", "tags": [], "advice": "The distance between the points $(x_1,y_1)$ and $(x_2,y_2)$ is $\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ units. This is the simply the length of the hypotenuse of the right angled triangle given by Pythagoras' Theorem $c^2=a^2+b^2$.
\n{diagram()}
\na) For the points $(\\var{x1},\\var{y1})$ and $(\\var{x2},\\var{y2})$ this is a distance of
\n$\\begin{align}\\sqrt{\\simplify[basic]{({x2}-{x1})^2+({y2}-{y1})^2}}&=\\sqrt{\\simplify[basic]{({x2-x1})^2+({y2-y1})^2}}\\\\&=\\sqrt{\\simplify[basic]{{(x2-x1)^2}+{(y2-y1)^2}}}\\\\&=\\sqrt{\\simplify[basic]{{(x2-x1)^2+(y2-y1)^2}}}\\\\&=\\var{triple[2]} \\quad \\text{units.}\\end{align}$
\n\nb) For the points $(\\var{xa1},\\var{ya1})$ and $(\\var{xa2},\\var{ya2})$ this is a distance of
\n$\\begin{align}\\sqrt{\\simplify[basic]{({xa2}-{xa1})^2+({ya2}-{ya1})^2}}&=\\sqrt{\\simplify[basic]{({xa2-xa1})^2+({ya2-ya1})^2}}\\\\&=\\sqrt{\\simplify[basic]{{(xa2-xa1)^2}+{(ya2-ya1)^2}}}\\\\&=\\sqrt{\\simplify[basic]{{(xa2-xa1)^2+(ya2-ya1)^2}}} \\quad \\text{units.}\\end{align}$
\n", "parts": [{"scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "marks": 0, "prompt": "The distance between the points $(\\var{x1},\\var{y1})$ and $(\\var{x2},\\var{y2})$ is [[0]] units.
\n\nNote: For this question your answer should be an integer.
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\n\nNote: For this question you can enter exact answers by using expressions such as sqrt(200) to indicate $\\sqrt{200}$.
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