Odpowiedź:
A = (3 , - 3 ) , B = (3 , 2 ) , C = (- 1 , 2 ) , D = (xd , yd)
xa = 3 , xb = 3 , xc = - 1 , ya = - 3 , yb = 2 , yc = 2
W prostokącie przekątne dzielą się na połowy
S - punkt środkowy = (xs , ys)
xs = (xa + xc)/2 = (3 - 1)/2 = 2/2 = 1
ys =(ya + yc)/2 = (- 3 + 2)/2 = - 1/2
S = ( 1 , - 1/2 )
xs = (xd + xb)/2
2 * xs = xd + xb
xd = 2 * xs - xb = 2 * 1 - 3 = 2 - 3 = - 1
ys = (yd + yb)/2
2 * ys = yd + yb
yd = 2 * ys - yb = 2 * (- 1/2) - 2 = - 1 - 2 = - 3
D = (- 1 , - 3 )
IABI = √[(xb - xa)² + (yb - ya)²] = √[(3 - 3)² + (2 + 3)²] = √(0² + 5²) =
= √25 = 5 [j]
[j] - znaczy właściwa jednostka
IADI = √[(xd - xa)² + (yd - ya)²] = √[(- 1 - 3)² + (- 3 + 3)²] = √[(- 4)² + 0²] =
= √16 = 4 [j]
o - obwód prostokąta = 2 * IABI + 2 * IACI = 2 * 5 + 2* 4 = 10[j] + 8[j] =
= 18 [j]
P - pole prostokąta = IABI * IADI = 5 * √8 = 40[j²]
