Find the factor of the Shear T T represents a  transformation.
$$T = \begin{bmatrix}
3 & -2 \\
2 & -1 \\
\end{bmatrix}$$
i) Find the invariant points for the transformation T.
Which I found to be  $$y = x$$
ii) T is a transformation called a shear. The line of shear is the line of invariant
points for the shear. The factor of a shear gives the distance a point is moved
as a multiple of its perpendicular distance from the line of shear. What is the
factor of the shear T?
I applied the point (1,0) to the transformation, giving me (3,2). Then, I found the distance between the two points which is $2\sqrt2$.
However, I'm unsure on how to find the perpendicular distance.  Additionally, I don't know what "as a multiple of its perpendicular distance from the line of the shear" means.
I tried plotting the points on the graph, with the line y = x. Dropping a perpendicular from the line to the points, however, I'm unsure on how to proceed.
Any guidance would be appreciated.

The distance from $(1,0)$ to the line $y=x$ is $\sqrt{2}/2$. The distance to its image is $2\sqrt{2}$ as you found out. Therefore the "factor of the shear" is $2\sqrt{2}\cdot 2/\sqrt{2}=4$.
