Question

unit 4 test
write a rule to describe each transformation.
1)
2)
graph the image of the figure using the transformation given.

1. translation: 3 units right and 1 unit up
2. translation: 2 units left and 6 units down
3. translation: 3 units left and 3 units up (w(-1, -4), v(0, 0), u(2, 0), t(1, -3))
4. translation: 4 units right and 3 units down (e(-5, 3), d(-3, 5), c(0, 2))

Explanation:

Step1: Recall translation rule

For a translation \(a\) units right and \(b\) units up, the rule for a point \((x,y)\) is \((x + a,y + b)\); for \(a\) units left and \(b\) units down, the rule is \((x - a,y - b)\).

Step2: Solve problem 3

The translation is 3 units right and 1 unit up. For a point \((x,y)\), the transformation rule is \((x+3,y + 1)\).

Step3: Solve problem 4

The translation is 2 units left and 6 units down. For a point \((x,y)\), the transformation rule is \((x - 2,y-6)\).

Step4: Solve problem 5

Given points \(W(-1,-4),V(0,0),U(2,0),T(1,-3)\). The translation is 3 units left and 3 units up. The new points:
For \(W(-1,-4)\): \(W'=(-1 - 3,-4 + 3)=(-4,-1)\)
For \(V(0,0)\): \(V'=(0 - 3,0 + 3)=(-3,3)\)
For \(U(2,0)\): \(U'=(2 - 3,0 + 3)=(-1,3)\)
For \(T(1,-3)\): \(T'=(1 - 3,-3 + 3)=(-2,0)\)

Step5: Solve problem 6

Given points \(E(-5,3),D(-3,5),C(0,2)\). The translation is 4 units right and 3 units down. The new points:
For \(E(-5,3)\): \(E'=(-5+4,3 - 3)=(-1,0)\)
For \(D(-3,5)\): \(D'=(-3 + 4,5 - 3)=(1,2)\)
For \(C(0,2)\): \(C'=(0+4,2 - 3)=(4,-1)\)

Answer:

1. Rule: \((x,y)\to(x + 3,y + 1)\)
2. Rule: \((x,y)\to(x - 2,y-6)\)
3. New points: \(W'(-4,-1),V'(-3,3),U'(-1,3),T'(-2,0)\)
4. New points: \(E'(-1,0),D'(1,2),C'(4,-1)\)