Question

ection 4: for #7 - 10 complete the table using the given transformation
le. then plot the points you found and draw the image.
transformation rule:
$(x,y)\to(x - 3,y - 5)$
pre - image
vertices
$c(-4,1)$
$s(-3,3)$
$r(-1,1)$
image
vertices

reflect $\triangle fgh$ over the line $y=-x$
pre - image
vertices
$f(4,2)$
$g(4,6)$
$h(6,2)$
image vertices

Explanation:

Step1: Apply the transformation rule \((x,y)\to(x - 3,y - 5)\)

For point \(C(-4,1)\):
\(x=-4,y = 1\)
\(x-3=-4-3=-7\)
\(y - 5=1-5=-4\)
The image vertex is \((-7,-4)\)

Step2: Apply the transformation rule \((x,y)\to(x - 3,y - 5)\)

For point \(S(-3,3)\):
\(x=-3,y = 3\)
\(x-3=-3-3=-6\)
\(y - 5=3-5=-2\)
The image vertex is \((-6,-2)\)

Step3: Apply the transformation rule \((x,y)\to(x - 3,y - 5)\)

For point \(R(-1,1)\):
\(x=-1,y = 1\)
\(x-3=-1-3=-4\)
\(y - 5=1-5=-4\)
The image vertex is \((-4,-4)\)

Step4: Apply the reflection rule over the line \(y=-x\) (the rule is \((x,y)\to(-y,-x)\))

For point \(F(4,2)\):
\(x = 4,y=2\)
\(-y=-2,-x=-4\)
The image vertex is \((-2,-4)\)

Step5: Apply the reflection rule over the line \(y=-x\) (the rule is \((x,y)\to(-y,-x)\))

For point \(G(4,6)\):
\(x = 4,y = 6\)
\(-y=-6,-x=-4\)
The image vertex is \((-6,-4)\)

Step6: Apply the reflection rule over the line \(y=-x\) (the rule is \((x,y)\to(-y,-x)\))

For point \(H(6,2)\):
\(x = 6,y=2\)
\(-y=-2,-x=-6\)
The image vertex is \((-2,-6)\)

Answer:

Pre - Image Vertices	Image Vertices
\(S(-3,3)\)	\((-6,-2)\)
\(R(-1,1)\)	\((-4,-4)\)
\(F(4,2)\)	\((-2,-4)\)
\(G(4,6)\)	\((-6,-4)\)
\(H(6,2)\)	\((-2,-6)\)