Sure, let's dilate the given triangle with a magnitude of 3.
Given the coordinates of the triangle:
[tex]\[ \begin{array}{rl}
\left[\begin{array}{ccc}
3 & 6 & 3 \\
-3 & 3 & 3
\end{array}\right]
\end{array} \][/tex]
1. Identify the original coordinates:
- [tex]\( (3, -3) \)[/tex]
- [tex]\( (6, 3) \)[/tex]
- [tex]\( (3, 3) \)[/tex]
2. Apply dilation with magnitude 3:
To dilate a point [tex]\( (x, y) \)[/tex] by a magnitude of 3, you multiply both coordinates by 3:
[tex]\[ (x', y') = (3x, 3y) \][/tex]
3. Calculate the new coordinates:
- For [tex]\( (3, -3) \)[/tex]:
[tex]\[ (x', y') = (3 \cdot 3, 3 \cdot -3) = (9, -9) \][/tex]
- For [tex]\( (6, 3) \)[/tex]:
[tex]\[ (x', y') = (3 \cdot 6, 3 \cdot 3) = (18, 9) \][/tex]
- For [tex]\( (3, 3) \)[/tex]:
[tex]\[ (x', y') = (3 \cdot 3, 3 \cdot 3) = (9, 9) \][/tex]
4. The new coordinates after dilation are:
- [tex]\( (9, -9) \)[/tex]
- [tex]\( (18, 9) \)[/tex]
- [tex]\( (9, 9) \)[/tex]
So, the table with the new coordinates becomes:
[tex]\[
\begin{array}{c}
\left[\begin{array}{ccc}
3 & 6 & 3 \\
-3 & 3 & 3
\end{array}\right]
\end{array}
\][/tex]
[tex]\[
\begin{array}{c}
\left[\begin{array}{ccc}
9 & 18 & 9 \\
-9 & 9 & 9
\end{array}\right]
\end{array}
\][/tex]
The transformed coordinates of the triangle are:
[tex]\[
\begin{array}{c}
\left[\begin{array}{ccc}
9 & 18 & 9 \\
-9 & 9 & 9
\end{array}\right]
\end{array}
\][/tex]
