To complete the translation [tex]\((x, y) \rightarrow (x-4, y)\)[/tex], we will subtract 4 from the [tex]\(x\)[/tex]-coordinate of each point while keeping the [tex]\(y\)[/tex]-coordinate the same.
Let's start with the points:
1. [tex]\( I(0, -3) \)[/tex]
2. [tex]\( J(0, -2) \)[/tex]
3. [tex]\( K(2, -2) \)[/tex]
4. [tex]\( L(4, -4) \)[/tex]
Step-by-Step Solution:
1. Point [tex]\( I(0, -3) \)[/tex]:
[tex]\[
x = 0 \quad \text{and} \quad y = -3
\][/tex]
Applying the translation [tex]\( (x - 4, y) \)[/tex]:
[tex]\[
x' = 0 - 4 = -4 \quad \text{and} \quad y' = -3
\][/tex]
So, [tex]\( I'(-4, -3) \)[/tex].
2. Point [tex]\( J(0, -2) \)[/tex]:
[tex]\[
x = 0 \quad \text{and} \quad y = -2
\][/tex]
Applying the translation [tex]\( (x - 4, y) \)[/tex]:
[tex]\[
x' = 0 - 4 = -4 \quad \text{and} \quad y' = -2
\][/tex]
So, [tex]\( J'(-4, -2) \)[/tex].
3. Point [tex]\( K(2, -2) \)[/tex]:
[tex]\[
x = 2 \quad \text{and} \quad y = -2
\][/tex]
Applying the translation [tex]\( (x - 4, y) \)[/tex]:
[tex]\[
x' = 2 - 4 = -2 \quad \text{and} \quad y' = -2
\][/tex]
So, [tex]\( K'(-2, -2) \)[/tex].
4. Point [tex]\( L(4, -4) \)[/tex]:
[tex]\[
x = 4 \quad \text{and} \quad y = -4
\][/tex]
Applying the translation [tex]\( (x - 4, y) \)[/tex]:
[tex]\[
x' = 4 - 4 = 0 \quad \text{and} \quad y' = -4
\][/tex]
So, [tex]\( L'(0, -4) \)[/tex].
Therefore, the translated coordinates are:
[tex]\[
\begin{array}{l}
I'(-4, -3) \\
J'(-4, -2) \\
K'(-2, -2) \\
L'(0, -4)
\end{array}
\][/tex]
These are the new positions of the points after the translation.
