Question

do the graphs below show a translation from the gray pre - image to the white image? explain why or why not.
1.
2.
3.
plot and connect the pre - image points listed in the table. translate each shape in the specified direction, list the new image coordinates, and rewrite the description as a rule.

1. translate to the right 2 units and up 6 units

pre - image | image | rule:
a(-5,-5) | a (, ) | (x,y)→(, )
b(-4,-2) | b (, )
c(-3,-5) | c (, )

1. translate to the right 6 units

pre - image | image | rule:
a(-4,2) | a (, ) | (x,y)→(, )
b(-5,3) | b (, )
c(-4,5) | c (, )
d(-3,3) | d (, )

1. without graphing, rewrite the coordinate (4,1) after each of the following transfor

a) shift right 5 units
b) shift left 3 units and down 2 units
c) (x,y)→(x - 1,y)
(4,1)→(, )
(4,1)→(, )
(4,1)→(, )

Explanation:

Step1: Recall translation rules

For a translation to the right \(h\) units and up \(k\) units, the rule is \((x,y)\to(x + h,y + k)\). For a translation to the right \(h\) units only, the rule is \((x,y)\to(x+h,y)\).

Step2: Solve problem 4

Given \(h = 2\) and \(k=6\).
For point \(A(-5,-5)\), \(A'=(-5 + 2,-5 + 6)=(-3,1)\).
For point \(B(-4,-2)\), \(B'=(-4 + 2,-2 + 6)=(-2,4)\).
For point \(C(-3,-5)\), \(C'=(-3 + 2,-5 + 6)=(-1,1)\).
The rule is \((x,y)\to(x + 2,y + 6)\).

Step3: Solve problem 5

Given \(h = 6\) and \(k = 0\).
For point \(A(-4,2)\), \(A'=(-4+6,2)=(2,2)\).
For point \(B(-5,3)\), \(B'=(-5 + 6,3)=(1,3)\).
For point \(C(-4,5)\), \(C'=(-4+6,5)=(2,5)\).
For point \(D(-3,3)\), \(D'=(-3+6,3)=(3,3)\).
The rule is \((x,y)\to(x + 6,y)\).

Step4: Solve problem 6a

Given a shift right 5 units (i.e., \(h = 5,k = 0\)), for the point \((4,1)\), the new point is \((4+5,1)=(9,1)\).

Step5: Solve problem 6b

Given a shift left 3 units (\(h=- 3\)) and down 2 units (\(k=-2\)), for the point \((4,1)\), the new point is \((4-3,1 - 2)=(1,-1)\).

Step6: Solve problem 6c

Given the rule \((x,y)\to(x - 1,y)\), for the point \((4,1)\), the new point is \((4-1,1)=(3,1)\).

Answer:

4.

Pre - Image	Image
\(B(-4,-2)\)	\(B'(-2,4)\)
\(C(-3,-5)\)	\(C'(-1,1)\)

Rule: \((x,y)\to(x + 2,y + 6)\)

5.

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

Rule: \((x,y)\to(x + 6,y)\)

6a. \((4,1)\to(9,1)\)
6b. \((4,1)\to(1,-1)\)
6c. \((4,1)\to(3,1)\)