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Sagot :
We have to find an original polygonal ADGL that, when tranlated and rotated, will give the polygonal with coordinates D (2,-6), L (3, 10), and G (7, - 4).
We have to do the trasnformation backwards for this problem.
We start with the rotation.
We can think of a rotation of 180 degrees, as it is easier.
In a rotation of 180 degrees the points with coordinates (x, y) became rotated points with coordinates (-x,-y).
Second step: we will think of a translation of one unit up in the vertical axis and one unit up in the horizontal axis.
This means that a point with coordinates (x.y) will became (x+1, y+1) after the translation.
So, for example the point D (2,-6). This is the point after the translation and rotation. So we have to work backwards.
First, previous to the rotation, we will have the point D'=(-2, -(-6))=(-2,6).
Second, previous to the translation, we should have D''=(-2-1,6-1)=(-3,5).
We can generalize this as:
Final point (x,y)
Previous to the rotation: (-x, -y)
Previous to the translation: (-x-1, -y-1)
So we have the points:
D=(2, -6) --> D''=(-2-1, 6-1)=(-3, 5)
L=(3, 10) --> L''=(-4,-11)
G=(7, -4) --> G''=(-8, 3)
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