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#11: History hidden by user avatar Tortilla‭ · 2023-09-20T07:11:22Z (8 months ago)
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Solely by eye, how can 16 year olds visually distinguish $\color{red}{\vec{b} - \vec{r}}$ from $\color{limegreen}{|\vec{b}| - |\vec{r}|}$ ?
Yearly, I teach 16 year olds the diagram beneath (improvement of [this original](https://math.stackexchange.com/a/774233)) that reappears on standardized tests _**with different letters,  orientation, position of the vectors**_. Tests require students to distinguish and label $\color{red}{\vec{b} - \vec{r}}$ _vs._ $\color{limegreen}{|\vec{b}| - |\vec{r}|}$. Despite my best endeavors, someone ALWAYS mixes them red and green, whenever this diagram resurfaces on tests!

#### How do you best explain their pictoric difference? How would you prevent this diagrammatic mix up BY EYE?


![](https://i.postimg.cc/Dys0bZwm/Reverse-Triangle-Inequality-Edited.jpg)
#10: Post edited by user avatar Tortilla‭ · 2023-09-20T07:11:22Z (8 months ago)

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#9: History hidden by user avatar Tortilla‭ · 2023-09-20T06:18:34Z (8 months ago)
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#8: Post edited by user avatar Tortilla‭ · 2023-09-20T06:18:34Z (8 months ago)

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#7: History hidden by user avatar Tortilla‭ · 2023-09-20T06:15:35Z (8 months ago)
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#6: Post edited by user avatar Tortilla‭ · 2023-09-20T06:15:35Z (8 months ago)

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#5: History hidden by user avatar Tortilla‭ · 2023-09-20T05:36:30Z (8 months ago)
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#4: Post edited by user avatar Tortilla‭ · 2023-09-20T05:36:30Z (8 months ago)

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#3: History hidden by user avatar Tortilla‭ · 2023-09-20T05:35:06Z (8 months ago)
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#2: Post edited by user avatar Tortilla‭ · 2023-09-20T05:35:06Z (8 months ago)

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#1: Initial revision by user avatar Tortilla‭ · 2023-09-20T05:32:39Z (8 months ago)

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