Question

22. A triangle has vertices (1,4), (1,1) and (-3, 1). The triangle is dilated by a scare factor of 2, then translated 5 units up, and then rotated 90* counterclockwise about the origin. What are the vertices of the image of the triangle?

The first step I took was to scale by 2. This made my coordinates (2,8), (2,2), (-6, 2)
The second step I took was to translate all of the (y) up 5 units. So that gave me (2,13), (2,7), and (-6, 7).
The third step was rotating the set counterclockwise at 90°, and i don't know how to do this. help! i will fan, and medal!

Answer 1

@e.mccormick @Hero

Answer 2

(-y,x)

You can also do this through a matrix:

\(\begin{bmatrix}
0 & -1\\
1 & 0
\end{bmatrix}\begin{bmatrix}
x_1\\
y_1
\end{bmatrix}
=\begin{bmatrix}
x_2\\
y_2
\end{bmatrix}\)

Where \(x_1, y_1\) is the input point and \(x_2,y_2\) is the output point.

For more on these types of matrices:
http://people.bath.ac.uk/sej20/transform.html