Rotate the shape; (-2,1),(0,1),(0,4),(-1,4),(-2,3) to 180 degrees counterclockwise

Answer 1

To rotate a point $(x,y)$ by 180 degrees counterclockwise around the origin, you can use the formula:

$$(x^{\prime },y^{\prime })=(-x,-y)$$

Now, let's apply this formula to each of the points you provided:

1. Point (-2, 1): $$(-(-2),-1)=(2,-1)$$

2. Point (0, 1): $$(-(0),-1)=(0,-1)$$

3. Point (0, 4): $$(-(0),-4)=(0,-4)$$

4. Point (-1, 4): $$(-(-1),-4)=(1,-4)$$

5. Point (-2, 3): $$(-(-2),-3)=(2,-3)$$

So, the rotated points are:

1. $(2,-1)$
2. $(0,-1)$
3. $(0,-4)$
4. $(1,-4)$
5. $(2,-3)$

Thus, the rotated shape has the vertices:

• $(2,-1)$
• $(0,-1)$
• $(0,-4)$
• $(1,-4)$
• $(2,-3)$