A tornado hit the area. It picked your house and rotated it 180 degrees counterclockwise.
Plot and state the points of your new house from Chapter 3 after a counterclockwise rotation of 180 degrees about the origin.
Is the new location of your house this transformation congruent to the neighbors house?
My house was (-4,0), (-4,4), (-2,6), (0,4), and (0,0)
The neighbors house is (4,0), (4,4) (2,6), (0,4) and (0,0)
To determine the new points of your house after a counterclockwise rotation of 180 degrees about the origin, we need to apply the transformation to each point individually.
Starting with your house's points:
(-4, 0) becomes (0, -4)
(-4, 4) becomes (-4, -4)
(-2, 6) becomes (-6, -2)
(0, 4) remains the same
(0, 0) remains the same
Therefore, the new points of your house after the rotation are:
(0, -4), (-4, -4), (-6, -2), (0, 4), and (0, 0).
To determine if the new location of your house is congruent to the neighbor's house, we need to check if the corresponding pairs of points have the same distance and direction. Comparing the coordinates, we can see that the neighborhoods house:
(4, 0) has the same distance and direction as (0, -4)
(4, 4) has the same distance and direction as (-4, -4)
(2, 6) has the same distance and direction as (-6, -2)
(0, 4) has the same distance and direction as (0, 4)
(0, 0) remains the same
Since all pairs of corresponding points have the same distances and directions, we can conclude that your new house's location after the rotation is congruent to the neighbor's house.