Answer :

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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