Question

a sequence of transformations on point (-8,3) are described.
$(x,y)\to(-y,x)$
$(x,y)\to(x + 1,y - 1)$
$(x,y)\to(-y,x)$
what is the x - value of the point after this sequence of transformations?
$x=$

Explanation:

Step1: Apply the first transformation \((x,y)\to(-y,x)\)

Given the point \((-9,3)\), for the transformation \((x,y)\to(-y,x)\), we substitute \(x = - 9\) and \(y = 3\).
So, \(-y=-3\) and \(x=-9\), the new point is \((-3,-9)\).

Step2: Apply the second transformation \((x,y)\to(x + 6,y-7)\)

For the point \((-3,-9)\) and the transformation \((x,y)\to(x + 6,y-7)\), we calculate:
\(x=-3+6 = 3\) and \(y=-9-7=-16\), the new point is \((3,-16)\).

Step3: Apply the third transformation \((x,y)\to(-y,x)\)

For the point \((3,-16)\) and the transformation \((x,y)\to(-y,x)\), we substitute \(x = 3\) and \(y=-16\).
So, \(-y = 16\) and \(x = 3\), the new point is \((16,3)\).

Answer:

\(16\)