Answer:
D' = (1, 3)
T' = (-5, 3)
Q' = (-5, -9)
E' = (1, -9)
Explanation:
To flip the house along a line going southwest-northeast through the center of the property, we can reflect the points across the line y = -x.
To reflect a point across a line, we can use the formula:
(x', y') = (xcos(2θ) + ysin(2θ), ycos(2θ) - xsin(2θ))
where θ is the angle between the x-axis and the line of reflection.
In this case, the line of reflection is y = -x, which has an angle of 45 degrees with the x-axis. Therefore, we have:
cos(2θ) = cos(90) = 0
sin(2θ) = sin(90) = 1
So the formula simplifies to:
(x', y') = (-y, -x)
Using this formula for each of the four corners of the house, we get:
D' = (-(-1), -(-3)) = (1, 3)
T' = (-(5), -(-3)) = (-5, 3)
Q' = (-(5), -(9)) = (-5, -9)
E' = (-(-1), -(9)) = (1, -9)
Therefore, the coordinates of the corners after the flip are:
D' = (1, 3)
T' = (-5, 3)
Q' = (-5, -9)
E' = (1, -9)
I hope this helps, I'm sorry if it didn't. I hope you do good on your test. If you need more help, ask me! :]