Vectors: Finding Coordinates 1

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Question statement

There are 3 points $A$, $B$, $C$, with position vectors \[ \mathbf a = \var{a},\quad \mathbf b = \var{b},\quad \mathbf c= \var{c} \]

respectively.

Find the coordinates of the point $D$ such that $ABCD$ forms a parallelogram.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	vector	vector(-2,-1)
b	vector	vector(1,3)
c	vector	vector(6,3)
d	vector	vector(3,-1)
defs	list	Nested 3×2 list

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
vector(random(-4..-2),random(-1..-2))

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `vector`

vector(-2,-1)

→ Used by:

d
defs

This variable doesn't seem to be used anywhere.

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$D =$ Unnamed gap

Advice

We want to find the position vector $\mathbf d = \vec{OD}$, such that $ABCD$ forms a parallelogram.

{geogebra_applet('https://www.geogebra.org/m/jqaptsj6',defs)}

For $ABCD$ to be a parallelogram, then $\vec{AB} = \vec{DC}$. In terms of the points' position vectors,

\[ \begin{split} \vec{AB} &\,= \mathbf b - \mathbf a &\,= \var{b-a} ,\\\\ \vec{DC} &\,= \mathbf c - \mathbf d &\,= \var{c} - \mathbf d. \end{split} \]

Therefore, \[ \begin{split} \var{b-a} &\,= \var{c} -\mathbf d \\ \implies \mathbf d &\,= \var{c+a-b}. \end{split}\]

Hence, the co-ordinates of $D$ are $(\var{d[0]},\var{d[1]})$.

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Jesus Ariza 10 months, 1 week ago

Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years ago

Error in variable testing condition

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Generated value: `vector`

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Vectors: Finding Coordinates 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jesus Ariza 10 months, 1 week ago

Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 4 years ago

Ben McGovern 4 years ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`