A pupil claims that $\overrightarrow{AB}=\overrightarrow{CD}$ proves that $A,B,C$ are

Question

A pupil claims that $\overrightarrow{AB}=\overrightarrow{CD}$ proves that $A,B,C$ are collinear. Consider $A(0,0),B(2,0),C(0,1),D(2,1)$. Show that the two vectors are equal.[1] Explain why these points disprove the pupil’s claim.[2]

Accepted Answer

(a) Both $\begin{pmatrix}2\ 0\end{pmatrix}$ (b) $C$ does not lie on $AB$

Testing a collinearity claim

Testing a collinearity claim

Solution:

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