I need help with two math problems.

Question

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

2. Use matrices to solve the system.
2x+3y=4
5x+8y=11

I appreciate the help!

Answer 1

1.
The transformations are:
e(O,2) : dilation about origin of 2 units
t(0,5) : translation 5 units up
r(y,-x) : rotation counter-clockwise 90°

So
(x,y)-> (2x,2y) -> (2x, 2y+5) -> (2y+5, -2x)

So combining it all:
(x,y) -> (2y+5, -2x)

2.
Using Cramer's rule:
Δ=8*2-3*5=1
x=(4*8-11*3)/Δ=-1
y=(2*11-5*4)/Δ=2
Check:
2(-1)+3*2=4
5(-1)+8*2=11
ok.

Answer 2

I'm still confused on the first one. Thank you. I appreciate it.

Answer 3

I need help