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The coordinates of the vertices of a triangle are P(3,1), Q(-3,4) and R(1,2). Calculate PQ, QR and PR.

October 12, 2026Mathematics

ScanSolve AI Answer

Step-by-step solution

3 steps

Here are the calculations for the vectors:

Given the coordinates of the vertices:
$P = (3,1)$
$Q = (-3,4)$
$R = (1,2)$

Calculate vector $\vec{PQ}$ .
To find $\vec{PQ}$ , subtract the coordinates of $P$ from the coordinates of $Q$ .
$\vec{PQ} = \begin{pmatrix} -3 - 3 \\ 4 - 1 \end{pmatrix}$ $\vec{PQ} = \begin{pmatrix} -6 \\ 3 \end{pmatrix}$
Calculate vector $\vec{QR}$ .
To find $\vec{QR}$ , subtract the coordinates of $Q$ from the coordinates of $R$ .
$\vec{QR} = \begin{pmatrix} 1 - (-3) \\ 2 - 4 \end{pmatrix}$ $\vec{QR} = \begin{pmatrix} 1 + 3 \\ -2 \end{pmatrix}$ $\vec{QR} = \begin{pmatrix} 4 \\ -2 \end{pmatrix}$
Calculate vector $\vec{PR}$ .
To find $\vec{PR}$ , subtract the coordinates of $P$ from the coordinates of $R$ .
$\vec{PR} = \begin{pmatrix} 1 - 3 \\ 2 - 1 \end{pmatrix}$ $\vec{PR} = \begin{pmatrix} -2 \\ 1 \end{pmatrix}$
The calculated vectors are:
$\boxed{\vec{PQ} = \begin{pmatrix} -6 \\ 3 \end{pmatrix}, \vec{QR} = \begin{pmatrix} 4 \\ -2 \end{pmatrix}, \vec{PR} = \begin{pmatrix} -2 \\ 1 \end{pmatrix}}$

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