41. Write a proof of the theorem that states if an angle of a quadrilateral is supplementary to both of its consecutive angles,
1 answer:
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Answer:
(-y, x)
Step-by-step explanation:
See the image attached.
We start with (x,y), this is, x in the abscissa axis and y in the ordinates axis. When we rotate it 90 degrees clock wise, the measure on the ordinates goes to the abscissa while the abscissa goes to the ordinates. You have to notice that this last movement is to the negative part of the ordinate axis. Here we pass from (x, y) to (y, -x).
Then you rotate again, going to a 180 degrees rotation in total. The movement is the same: ordinates values go to the abscissa value. So, the -x that was on ordinates goes to the abscissa and the y in the abscissa goes to ordinates. However this last movement implies a negative sign in the y value, as we are going from positive to negative values. So, we pass from (y, -x) yo (-x, -y).
Finally we move again for reaching the 270 degrees rotation. Similar to the last 2 movements, -x passes from abscissa to ordinates and becoming x as we the sign is positive. In the same way, the -y in the ordinates goes to the abscissa and still being -y as we still on negative values. So, we finish with (-y, x).
So, this is the final answer: (-y, x)
Here I also attach a numerical example.
