Mathematics

Problem

For the triangle

DEF

with

D(-1,2)

E(3,5)

and

F(2,-1)

, a linear transformation

T

is represented by the matrix

\begin{pmatrix}0&-1\\1&0\end{pmatrix}

. Find the area of the triangle

T(DEF)

(in square units).

Intuitive explanation

Linear transformations preserve or scale area in a predictable way—the key is the determinant of the transformation matrix. Instead of finding the new coordinates and recalculating, you can use the fact that areas scale by the absolute value of the determinant. First find the area of the original triangle $DEF$ using the coordinate formula, then multiply by $|\det(T)|$ to get the transformed area.

Intuitive explanation

Browse the problem library