Certainly! Let's apply the translation [tex]\( T(4, -3) \)[/tex] to the given ordered pairs [tex]\((-9, 2)\)[/tex] and [tex]\((0, -5)\)[/tex].
Translation involves adding the components of the translation vector to each corresponding component of the original points.
### Step-by-Step Solution:
1. Original Ordered Pairs:
- Pair 1: [tex]\((-9, 2)\)[/tex]
- Pair 2: [tex]\((0, -5)\)[/tex]
2. Translation Vector: [tex]\(T(4, -3)\)[/tex]
This means we will translate (or shift) each point by adding 4 to the x-component and subtracting 3 from the y-component.
3. Translation of the First Pair:
- Original pair: [tex]\((-9, 2)\)[/tex]
- Apply translation [tex]\(T(4, -3)\)[/tex]:
- New x-coordinate: [tex]\(-9 + 4 = -5\)[/tex]
- New y-coordinate: [tex]\(2 - 3 = -1\)[/tex]
- Translated Pair 1: [tex]\((-5, -1)\)[/tex]
4. Translation of the Second Pair:
- Original pair: [tex]\((0, -5)\)[/tex]
- Apply translation [tex]\(T(4, -3)\)[/tex]:
- New x-coordinate: [tex]\(0 + 4 = 4\)[/tex]
- New y-coordinate: [tex]\(-5 - 3 = -8\)[/tex]
- Translated Pair 2: [tex]\((4, -8)\)[/tex]
So, after applying the translation [tex]\( T(4, -3) \)[/tex], the new coordinates are:
- The transformed point from [tex]\((-9, 2)\)[/tex] is [tex]\((-5, -1)\)[/tex].
- The transformed point from [tex]\((0, -5)\)[/tex] is [tex]\((4, -8)\)[/tex].
Thus, the translated pairs are:
[tex]\[ (-5, -1) \quad \text{and} \quad (4, -8) \][/tex]
