Question

A triangle is rotated 180 degrees about the origin. Its image is reflected in the x-axis. The vertices of the final triangle are (-4,-4), (-2, -4), and (-3, -1). What are the vertices of the original triangle?

Answer 1

Hello!
So in this question, you need to do it backwards. This means, taking the vertices of the new triangle and reflecting it across the X axis, and then reflecting it 180 degrees.
The formula for reflecting across the X axis is--
(X,Y) -> (X,-Y) *Note, in this case, it may not always be negative Y. The                                  negative symbol only stands for the opposite. So it the                                    point is negative originally, then the new point would be                                  positive.
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So, now you take your points, and use the formula.
(-4,-4) -> (-4,4)
(-2,-4) -> (-2,4)
(-3,-1) -> (-3,1)
Now, you have your new points. But, you still need to rotate it 180 degrees.
The formula to rotate 180 degrees is--
(X,Y) -> (-X,-Y)
Then, you take your new points, and use the formula for each coordinate.
(-4,4) -> (4,-4)
(-2,4) -> (2,-4)
(-3,1) -> (3,-1)
There is your answer. The new points would be--
(4,-4)
(2,-4)
(3,-1)
Hope this helped!
Regards,
~KayEmQue