Question

1. a sequence of transformations on point (-8,3) are described.

$(x,y)\to(-y,-x)$
$(x,y)\to(x + 2,y - 1)$
$(x,y)\to(-y,x)$
what is the x - value of the point after this sequence of transformations?
$x=\square$

Explanation:

Step1: Apply the first transformation

Given \((x,y)=(-8,3)\) and the transformation \((x,y)\to(-y,-x)\).
Substitute \(x = - 8\) and \(y = 3\) into \((-y,-x)\):
\(x_1=-y=-3\), \(y_1=-x = 8\)
The point becomes \((-3,8)\)

Step2: Apply the second transformation

Take the point \((-3,8)\) and use the transformation \((x,y)\to(x + 2,y-1)\)
Substitute \(x=-3\) and \(y = 8\) into \((x + 2,y-1)\):
\(x_2=-3+2=-1\), \(y_2=8 - 1=7\)
The point becomes \((-1,7)\)

Step3: Apply the third transformation

Take the point \((-1,7)\) and use the transformation \((x,y)\to(-y,x)\)
Substitute \(x=-1\) and \(y = 7\) into \((-y,x)\):
\(x_3=-y=-7\)

Answer:

\(-7\)