Suppose the function $f(x)$ is defined on the domain $\{x_1,x_2,x_3\}$, so that the graph of $y=f(x)$ consists of just three points. Suppose those three points form a triangle of area $32$.

The graph of $y = 2f(2x)$ also consists of just three points. What is the area of the triangle formed by those three points?

Guest Mar 27, 2019

edited by
Guest
Mar 27, 2019

edited by Guest Mar 27, 2019

edited by Guest Mar 27, 2019

#1**+1 **

\(\text{Each of your new points is derived as }\\ (x^\prime_k,y^\prime_k) = \begin{pmatrix}\frac 1 2 &0 \\0 &2\end{pmatrix}\begin{pmatrix}x_k\\y_k\end{pmatrix}\)

\(\text{This results in an overall transformation matrix of }\\ \begin{pmatrix} \frac 1 2 &0 &0 &0 &0 &0\\ 0 &2 &0 &0 &0 &0 \\ 0 &0 &\frac 1 2 &0 &0 &0\\ 0 &0 &0 &2 &0 &0 \\ 0 &0 &0 &0 &\frac 1 2 &0 \\ 0 &0 &0 &0 &0 &2 \end{pmatrix}\)

\(\text{The determinant of this matrix is simply the product of the diagonal terms and equals }1\\ \text{Thus the transformation will leave the original area unchanged}\)

.Rom Mar 27, 2019