(2, -1)

Question

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

After an 180 degree turn, what are the plot points? Are the new plot points congruent to the original? Is it congruent to the figure (-2, -1) (0, -1) (0, -3) (-1, -4) (-2, -3)

Answer 1

To determine the new plot points after a 180-degree turn, we can visualize the transformation. A 180-degree rotation around the origin changes each point $(x,y)$ to $(-x,-y)$.

Let's apply this transformation to the given points:

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

So the new plot points after the 180-degree turn are:

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

Next, we can see if the new plot points are congruent to the original points.

Congruence in geometry means that two shapes have the same size and shape. A 180-degree rotation preserves distance and angle measures, so the new points will be congruent to the original figure.

Finally, we need to check if the new points are congruent to the figure $(-2,-1),(0,-1),(0,-3),(-1,-4),(-2,-3)$ given in the question. To check for congruence, we can compare the sets of points:

1. The point $(-2,1)$ does not match any points in the given figure.
2. The point $(0,1)$ does not match any points in the given figure.
3. The point $(0,3)$ does not match any points in the given figure.
4. The point $(-1,4)$ does not match any points in the given figure.
5. The point $(-2,3)$ does not match any points in the given figure.

Since none of the new points match those given in the figure $(-2,-1),(0,-1),(0,-3),(-1,-4),(-2,-3)$, they are not congruent to that figure.

In summary:

• New plot points after a 180-degree rotation: $(-2,1),(0,1),(0,3),(-1,4),(-2,3)$
• New plot points are congruent to the original points.
• New plot points are NOT congruent to the figure $(-2,-1),(0,-1),(0,-3),(-1,-4),(-2,-3)$.