Can somebody PLEASE help me with this math question? D:

Question

I cant seem to figure it out:

 

ABC has vertices A(0,2), B(-3, -2), and C(2, -4). What are the coordinates of the image of ABC after it has been reflected using the reflection matrix: -1 0

                                         0 1

 

 

 

 

 

A) A' (0,2) B'(-3, -4), C' (-2, -4)

 

B) A' (0,-2), B' (-3,2) C' (2,4)

Answer 1

The matrix [-1 0; 0 1] is a reflection on the y-axis.

Any easy way to do this is to look at one point like A.

A=(0,2) If we flip this over the y-axis the x value should become negative but the y value should not change.

 

You can also do the dot product to figure this out.

A'=(0,2). [-1 0; 0 1] B'=(-3, -2).[-1 0; 0 1] and C'=(2, -4).[-1 0; 0 1]

A'=(0.-1,2.0)+(0.0,2.1) B'=(-3.-1, -2.0)+(-3.0, -2.1) and C'=(2.-1, -4.0)+(2.0, -4.1)

A'=(0,0)+(0,2) B'=(3, 0)+(0, 2) and C'=(-2, 0)+(0, -4)

A'=(0,2) B'=(3, 2) and C'=(-2, -4)

So the correct answer is not there.

 

If the matrix is suppose to be [1 0; 0 -1] it is a reflection on the x-axis.
A=(0,2) If we flip this over the x-axis the y value should become negative but the x value should not change.
So the correct answer is B.