9514 1404 393
Answer:
a) M(2,2), B(4, -2), D(0, 6)
b) 40
Step-by-step explanation:
a) The midpoint of AC is the average of the endpoint coordinates.
M = (A +C)/2
M = ((-2, 0) +(6, 4))/2 = (4, 4)/2
M = (2, 2)
There are several ways to find points B and D. One of them is to rotate points A and C 90° about M. The 90° CCW rotation transformation about the origin is ...
(x, y) ⇒ (-y, x)
About the point (2, 2), the transformation would be ...
(x, y) ⇒ (-(y -2)+2, (x -2)+2) = (4 -y, x)
Rotating point A 90° to get point B, we have ...
B = (4 -0, -2)
B = (4, -2)
And rotating C to get point D, we have ...
D = (4 -4, 6)
D = (0, 6)
__
b) The area of the square is half the square of the diagonal. The square of the diagonal can be found using the distance formula ...
d² = AC² = (6-(-2))² +(4 -0)² = 64 +16 = 80
Then the area is ...
area = AC²/2 = 80/2
area = 40 . . . . square units
