Question

find the coordinates of the vertices of the polygon after the given translation to a new position in the plane. original point translated point (-3,6) (x,y)=(2,3)× (-5,3) (x,y)=(2,-5)× (-1,3) (x,y)=(4,0)× (-3,0) (x,y)=(4,-3)×

Explanation:

Step1: Identify translation rule

The polygon is translated 6 units right and 3 units down. For a point $(x,y)$, the new - point after translation is $(x + 6,y-3)$.

Step2: Translate point $(-3,6)$

For the point $(-3,6)$, $x=-3$ and $y = 6$. Using the translation rule $(x + 6,y - 3)$, we have $x=-3+6 = 3$ and $y=6 - 3=3$. So the new point is $(3,3)$.

Step3: Translate point $(-5,3)$

For the point $(-5,3)$, $x=-5$ and $y = 3$. Using the translation rule $(x + 6,y - 3)$, we have $x=-5+6 = 1$ and $y=3 - 3=0$. So the new point is $(1,0)$.

Step4: Translate point $(-1,3)$

For the point $(-1,3)$, $x=-1$ and $y = 3$. Using the translation rule $(x + 6,y - 3)$, we have $x=-1+6 = 5$ and $y=3 - 3=0$. So the new point is $(5,0)$.

Step5: Translate point $(-3,0)$

For the point $(-3,0)$, $x=-3$ and $y = 0$. Using the translation rule $(x + 6,y - 3)$, we have $x=-3+6 = 3$ and $y=0 - 3=-3$. So the new point is $(3,-3)$.

Answer:

Original Point	Translated Point
$(-5,3)$	$(1,0)$
$(-1,3)$	$(5,0)$
$(-3,0)$	$(3,-3)$