2026-09-10T00:15:23.261047 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL Calculate the column vector \(\overrightarrow{AB}...
Question 1 Report
Calculate the column vector \(\overrightarrow{AB}\), where \(A\) is the point \((2, 9)\) and \(B\) is the point \((10, 3)\), as shown on the grid. Then work out the length of \(AB\). Give the length as a whole number.
Answer Details
A vector from \(A\) to \(B\) is found by subtracting the coordinates of \(A\) from the corresponding coordinates of \(B\):
\[\overrightarrow{AB}=\begin{pmatrix}10-2\\3-9\end{pmatrix}=\begin{pmatrix}8\\-6\end{pmatrix}.\]
Its length is found using Pythagoras’ theorem:
\[AB=\sqrt{8^2+(-6)^2}=\sqrt{64+36}=\sqrt{100}=10.\]
Therefore \(\overrightarrow{AB}=\begin{pmatrix}8\\-6\end{pmatrix}\) and \(AB=\mathbf{10}\). [4 marks]
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