// Numbas version: finer_feedback_settings {"name": "Linear graphs: Calculate length of a line segment", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Linear graphs: Calculate length of a line segment", "tags": ["Category: Linear Graphs"], "metadata": {"description": "

Calculate the length of a line segment given two points

", "licence": "None specified"}, "statement": "

Find the length of the line segment between:

\n

$(\\var{ax},\\var{ay})$ and $(\\var{bx}, \\var{by})$.

", "advice": "

The best way to answer this question is using Pythagoras' Theorem $a^2 + b^2 = c^2$ and a sketch.

\n

{app2}

Use the given points as two vertices and create a right angled triangle:

{app1}

\n

\\[ \\begin{split}

&\\, a^2 + b^2 = c^2 \\\\ 
&\\,  (\\var{bx} - \\var{ax})^2 + (\\var{by} - \\var{ay})^2 = c^2 \\\\
&\\, (\\var{bx-ax})^2 + (\\var{by-ay})^2 = c^2 \\\\
&\\, \\var{(ax-bx)^2 + (ay-by)^2} = c^2 \\\\ 
&\\,\\sqrt{\\var{(ax-bx)^2 + (ay-by)^2}}= c \\\\
&\\,\\var{sqrt((ax-bx)^2 + (ay-by)^2)}= c \\\\
&\\, c = \\var{csimp}  \\text{ units} \\\\
\\end{split} \\]

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