Your house: A (4, 4), B (8, 4), C (8, 8), D (6, 10), E (4, 8)
Because you are famous, people want to live near you. You have a new neighbor move in across the street after they build the same exact house as you did. state the points of your neighbor's house, which is a reflection of your house over the y-axis.
The coordinates of your neighbor's house, which is a reflection of your house over the y-axis, would be:
A' (-4, 4)
B' (-8, 4)
C' (-8, 8)
D' (-6, 10)
E' (-4, 8)
Is your neighbors house after this transformation congruent to your house? Explain your answer
Yes, after the reflection over the y-axis, your neighbor's house is congruent to your house. Congruence means that two figures have the same shape and size, and in this case, both houses have the same shape and size as they are mirror images of each other. The distances between corresponding points, such as A and A', B and B', etc., remain the same, indicating congruence.
can you giver a longer answer?
Certainly! When two figures are congruent, it means that they have the exact same shape and size, and all corresponding angles and sides are equal.
In this case, your neighbor's house is a reflection of your house over the y-axis. Reflection over the y-axis simply flips the figure horizontally. All the points in your house are reflected across the y-axis to create the corresponding points in your neighbor's house.
For example, let's consider the point A (4, 4) in your house. After reflecting it over the y-axis, it becomes A' (-4, 4) in your neighbor's house. Similarly, point B (8, 4) in your house becomes B' (-8, 4) in your neighbor's house, and so on for points C, D, and E.
Since the distances and angles between corresponding points remain the same after the reflection, it shows that your house and your neighbor's house have the same shape and size. Therefore, they are congruent to each other.
In summary, your neighbor's house is congruent to your house after the reflection over the y-axis because they have the same shape, size, and all corresponding angles and sides are equal.
A tornado hit the area. It picked up your house and rotated it 180 degrees counterclockwise.
State the points of your new house after a counterclockwise rotation of 180 degrees about the origin.
To find the points of your new house after a counterclockwise rotation of 180 degrees about the origin, we can apply the rotation transformation to each point of your original house coordinates.
Applying the counterclockwise rotation of 180 degrees about the origin to each point, the new coordinates of your house would be:
A' (-4, -4)
B' (-8, -4)
C' (-8, -8)
D' (-6, -10)
E' (-4, -8)
These new coordinates represent the points of your new house after it has been rotated 180 degrees counterclockwise about the origin due to the tornado.
Is the new location of your house after this transformation congruent to the neighbor's house in Chapter 4? Explain your answer.
No, the new location of your house after the counterclockwise rotation of 180 degrees about the origin is not congruent to the neighbor's house in Chapter 4. Congruence means that two figures have the same shape and size, with equal corresponding angles and sides.
In Chapter 4, we reflected your house over the y-axis to determine the coordinates of the neighbor's house. However, in this case, we are rotating your house 180 degrees counterclockwise about the origin. Rotation changes the orientation of the figure, but keeps the shape and size the same.
The reflection and rotation transformations are different, resulting in different coordinates for the new locations of the houses. Therefore, the new location of your house after the rotation is not congruent to the neighbor's house in Chapter 4.