Question 8
Is the new location of your house after this transformation congruent to the neighbor’s house in Chapter 3? Explain your answer.
Since we do not have access to the specific transformation described in Chapter 3, we cannot determine if the new location of the house is congruent to the neighbor's house. In order to determine congruence, we would need to know the specific transformation applied (e.g. translation, rotation, reflection) and the corresponding measurements and angles involved. Without this information, we cannot accurately compare the two houses and determine if they are congruent.
House from chapter 3: (-2,-1) (0,-1) (-2,-3) (0,-3) (-1,-4)
House after transformation: (2,-1) (2,-3) (1,-4) (0,-3) (0,-1)
Based on the given coordinates, we can determine if the new location of the house after the transformation is congruent to the neighbor's house in Chapter 3.
Comparing corresponding vertices:
(2,-1) and (-2,-1) - The x-coordinates are different, so it is not congruent.
(2,-3) and (-2,-3) - The x-coordinates are different, so it is not congruent.
(1,-4) and (-1,-4) - The x-coordinates are different, so it is not congruent.
(0,-3) and (0,-3) - The coordinates are the same, so it is congruent.
(0,-1) and (0,-1) - The coordinates are the same, so it is congruent.
Since the new location of the house after the transformation has two pairs of corresponding vertices that are congruent to the neighbor's house in Chapter 3, we can conclude that the two houses are congruent.