Question

plot and connect the pre - image points listed in the table. translate each shape according to the rule provided, list the new image coordinates, and rewrite the rule as a description.

1. (x,y)→(x,y - 4)

pre - image image
a(2,2) a( , )
b(1,4) b( , )
c(5,5) c( , )

1. (x,y)→(x - 6,y + 4)

pre - image image
a(2,-5) a( , )
b(2,-3) b( , )
c(4,-3) c( , )
d(5,-5) d( , )
write a description and a rule for each translation shown below. the gray shape is the pre - image, and the white shape is the new image.

1. description: rule:
2. description: rule:

write a translation that will translate the triangle into the first quadrant. test your translation on the graph and write your translation as a description and as a rule.
description: rule:

1. write a translation that will translate the rectangle into the first quadrant. test your translation on the graph and write your translation as a description and as a rule.

description: rule:

Explanation:

Step1: Apply translation rule for point A in first table

Given rule $(x,y)\to(x,y - 4)$ and $A(2,2)$. For the x - coordinate, it remains the same ($x = 2$), and for the y - coordinate, $y-4=2 - 4=-2$. So $A'(2,-2)$.

Step2: Apply translation rule for point B in first table

Given $B(1,4)$ and rule $(x,y)\to(x,y - 4)$. The x - coordinate remains $x = 1$, and $y-4=4 - 4 = 0$. So $B'(1,0)$.

Step3: Apply translation rule for point C in first table

Given $C(5,5)$ and rule $(x,y)\to(x,y - 4)$. The x - coordinate remains $x = 5$, and $y-4=5 - 4=1$. So $C'(5,1)$.

Step4: Apply translation rule for point A in second table

Given rule $(x,y)\to(x - 6,y + 4)$ and $A(2,-5)$. The new x - coordinate is $x-6=2-6=-4$, and the new y - coordinate is $y + 4=-5 + 4=-1$. So $A'(-4,-1)$.

Step5: Apply translation rule for point B in second table

Given $B(2,-3)$ and rule $(x,y)\to(x - 6,y + 4)$. The new x - coordinate is $x-6=2-6=-4$, and the new y - coordinate is $y + 4=-3 + 4 = 1$. So $B'(-4,1)$.

Step6: Apply translation rule for point C in second table

Given $C(4,-3)$ and rule $(x,y)\to(x - 6,y + 4)$. The new x - coordinate is $x-6=4-6=-2$, and the new y - coordinate is $y + 4=-3 + 4=1$. So $C'(-2,1)$.

Step7: Apply translation rule for point D in second table

Given $D(5,-5)$ and rule $(x,y)\to(x - 6,y + 4)$. The new x - coordinate is $x-6=5-6=-1$, and the new y - coordinate is $y + 4=-5 + 4=-1$. So $D'(-1,-1)$.

Answer:

Pre - Image	Image
B(1,4)	B'(1,0)
C(5,5)	C'(5,1)
A(2,-5)	A'(-4,-1)
B(2,-3)	B'(-4,1)
C(4,-3)	C'(-2,1)
D(5,-5)	D'(-1,-1)