Standard +0.3 This question requires finding the area of the original triangle T, applying the determinant property that area scales by |det(M)|, and solving for k. While it combines coordinate geometry with matrix transformations, it's a straightforward application of standard Further Maths techniques with no conceptual surprises—slightly easier than average for FM Pure.
The triangle \(T\) has vertices at the points \((1, k)\), \((3,0)\) and \((11,0)\), where \(k\) is a positive constant. Triangle \(T\) is transformed onto the triangle \(T'\) by the matrix
$$\begin{pmatrix} 6 & -2 \\ 1 & 2 \end{pmatrix}$$
Given that the area of triangle \(T'\) is 364 square units, find the value of \(k\). [4]
The triangle $T$ has vertices at the points $(1, k)$, $(3,0)$ and $(11,0)$, where $k$ is a positive constant. Triangle $T$ is transformed onto the triangle $T'$ by the matrix
$$\begin{pmatrix} 6 & -2 \\ 1 & 2 \end{pmatrix}$$
Given that the area of triangle $T'$ is 364 square units, find the value of $k$. [4]
\hfill \mbox{\textit{SPS SPS FM Pure 2022 Q5 [4]}}