Help with triangle vertices this is linear algebra?

Question

The question is use the triangle with vertices (1,1), (5,1), and (3,3). Write the transformation that best describes the move to the given vertices. (1,5), (5,5), and (3,3).

Answer 1

Did you graph the coordinates? It looks like a reflection over the line y = 3...

(1,1) --> (1,5)
(5,1) --> (5,5)
(3,3) --> (3,3)

T(x, y) = (x, 6-y)

Answer 2

x → x
y → ay + b
a + b = 5
3a + b = 3
ie a + b = 1
So a = -1, b = 6

So
(x, y) → (x, -y + 6)

This is a reflection in the x-axis followed by a vertical translation 6 units up)

ie (x, y) → (x, -y) → (x, -y + 6)


So
(1. 0)(x y) + (0 6) → (x -y+6)
(0 -1)