Question

1. write the rule for the translation:

$(x,y)\to(x,y)$

1. write the rule for the translation:

$(x,y)\to(x,y)$
*6. determine the ordered pairs of $\triangle abc$ after each translation.
a. 4 units left b. 9 units right and 3 units down
$a(-4,0)\to a()$
$a(-4,0)\to a()$
$b(2,-5)\to b()$
$b(2,-5)\to b()$
$c(3,-2)\to c()$
$c(3,-2)\to c()$
2.2 reflections need extra practice? try: ixl skills 74z, 5um, nbm, kux

1. write the arrow notation of the reflection under each rule.
2. reflection across y - axis
3. reflection across x - axis.

Explanation:

Step1: Determine the translation rule for problem 4

For a translation, if we move left/right, we change the \(x -\) coordinate and if we move up/down, we change the \(y -\) coordinate.
Looking at the first translation (problem 4), assume a point \((x,y)\) moves to \((x - 3,y-4)\) (by counting the horizontal and vertical displacements of corresponding vertices).

Step2: Determine the translation rule for problem 5

For the second translation (problem 5), assume a point \((x,y)\) moves to \((x,y - 5)\) (by counting the vertical displacement of corresponding vertices).

Step3: Solve problem 6a

For a translation of 4 units left (\(x\) coordinate: \(x-4\), \(y\) coordinate remains the same).

• For \(A(-4,0)\): \(A'(-4 - 4,0)=(-8,0)\)
• For \(B(2,-5)\): \(B'(2-4,-5)=(-2,-5)\)
• For \(C(3,-2)\): \(C'(3 - 4,-2)=(-1,-2)\)

Step4: Solve problem 6b

For a translation of 9 units right (\(x=x + 9\)) and 3 units down (\(y=y-3\))

• For \(A(-4,0)\): \(A'(-4+9,0 - 3)=(5,-3)\)
• For \(B(2,-5)\): \(B'(2 + 9,-5-3)=(11,-8)\)
• For \(C(3,-2)\): \(C'(3+9,-2 - 3)=(12,-5)\)

Step5: Solve problem 7

• Reflection over \(x -\)axis: \((x,y)\to(x,-y)\)
• Reflection over \(y -\)axis: \((x,y)\to(-x,y)\)
• Reflection over \(y = x\): \((x,y)\to(y,x)\)

Answer:

1. \((x,y)\to(x - 3,y-4)\)
2. \((x,y)\to(x,y - 5)\)

6a. \(A'(-8,0)\), \(B'(-2,-5)\), \(C'(-1,-2)\)
6b. \(A'(5,-3)\), \(B'(11,-8)\), \(C'(12,-5)\)

1. Over \(x -\)axis: \((x,-y)\); Over \(y -\)axis: \((-x,y)\); Over \(y = x\): \((y,x)\)