Posted by **Kelly** on Sunday, May 19, 2013 at 12:10am.

I need help with two math problems.

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!

- Algebra -
**MathMate**, Sunday, May 19, 2013 at 8:05am
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.

- Algebra -
**Melania**, Sunday, May 19, 2013 at 11:17am
I'm still confused on the first one. Thank you. I appreciate it.

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