Given that \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix}\) and \(AC = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\), find |BC|.
Question 1 Report
Given that \(AB = \begin{pmatrix} 4 \\ 3 \end{pmatrix}\) and \(AC = \begin{pmatrix} 2 \\ -3 \end{pmatrix}\), find |BC|.
Answer Details
To find the length of BC, we need to first find the coordinates of point B and point C.
Point B is given as AB = (4, 3).
To find point C, we can use the fact that AC + CB = AB.
Rearranging, we get CB = AB - AC.
Substituting the values we get,
CB = \(\begin{pmatrix} 4 \\ 3 \end{pmatrix}\) - \(\begin{pmatrix} 2 \\ -3 \end{pmatrix}\) = \(\begin{pmatrix} 2 \\ 6 \end{pmatrix}\)
The length of BC is then given by the formula:
|BC| = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of points B and C respectively.
Substituting the values we get,
|BC| = √((2 - 0)² + (6 - 0)²) = √(4 + 36) = √40 = 2√10
Therefore, the length of BC is 2√10, which is option C.
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