Under what condition is a transformation T(x,y)=(ax+by+e,cx+dy+f)T(x, y) = (ax + by + e, cx + dy + f)T(x,y)=(ax+by+e,cx+dy+f) an isometry?
a2+c2=1,b2+d2=1,ab+cd=0a^2 + c^2 = 1, b^2 + d^2 = 1, ab + cd = 0a2+c2=1,b2+d2=1,ab+cd=0
ad−bc=1ad - bc = 1ad−bc=1
a=d,b=−ca = d, b = -ca=d,b=−c
a+d=0a + d = 0a+d=0