How to solve a variable?
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To solve for x in terms of b, simply treat b as a number, and solve for x as usual: first of all, we expand the left hand side:
Subtract 10 from both sides:
Divide both sides by -2b:
This means that in particular, if we set , we have
Before we proceed on determining the transformation happening on this problem, it's better to see first the location of the figure by drawing it in a cartesian coordinate plane. We have
If we observe the figures and the coordinates of the plot, we can see that there is a difference of 1 on the x coordinates of P and y coordinates of Q. Therefore, the first transformation that we consider here is the movement of figure P by 1 unit to the left. We have
This transformation changes the location of figure P into
The next transformation will be the rotation of the red dotted figure on the figure above by 90 degrees counterclockwise. With this transformation, the coordinates will transform as
Hence, for the rotation, we have the new coordinates.
The transformed image, which is represented as NMPO, will now be at
For the last transformation, we will be reflecting the figure NMPO over the <em>y</em> axis. This changes the coordinates as
We now have the new coordinates:
As you can see, they have the same coordinates as figure Q.
The mapping rules for the sequence described above are as follows:
First transformation (moving one unit to the left (x-1,y))
Second transformation (rotation counter clockwise (-y,x))
Third Transformation (reflection over y-axis (-x,y))
