Answer:
To rotate the point \((-5, -1)\) 270 degrees counterclockwise around the origin, we can use the following rules for rotation transformations:
- A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.
- For a 90-degree clockwise rotation of a point \((x, y)\), the new coordinates are \((y, -x)\).
Given the point \((-5, -1)\):
1. The x-coordinate is \(-5\) and the y-coordinate is \(-1\).
2. Applying the 90-degree clockwise rotation transformation:
\[ (y, -x) \]
Substituting \((-5, -1)\):
\[ (-1, -(-5)) \]
This simplifies to:
\[ (-1, 5) \]
So, the point \((-5, -1)\) after a 270-degree counterclockwise rotation becomes \((-1, 5)\).
Here is the graphical representation of the rotation:
```
Initial Point (-5, -1)
Rotated Point (-1, 5)
y
|
5-+ *
|
4-+
|
3-+
|
2-+
|
1-+
|
0-+--+--+--+--+--+--+--+--+--+--+--+--+--+-- x
-5 -4 -3 -2 -1 0 1 2 3 4 5
|
-1-+ *
|
-2-+
|
-3-+
|
-4-+
|
-5-+
```
In the graph:
- The point marked with a "*" at \((-5, -1)\) is the initial point.
- The point marked with a "*" at \((-1, 5)\) is the point after the 270-degree counterclockwise rotation.
Step-by-step explanation:
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