Given points #A(5,2) , B (4,2)#
Reflected across #x = -3#, #y = -5#
![Given points #A(5,2) , B (4,2)#
Reflected across #x = -3#, #y = -5#
#A (x,y) -> A’(x, y) = (5,2) -> ((2x’ - 5), (2y’ - 2)) => (-11, -12)#
#A’(x,y) => ((-6 - 5), (-10 - 2)) => (-11, -12)#
#B (x,y) - > B’ (x,y) = (4 , 2) -> ((2x’ - 4), (2y’ - 2)) #
#B’(x,y) => ((-6 - 4), (-10 - 2)) => (-10, -12)#
New coordinates after reflection are #A’(-11, -12), B’(-10, -12)#
Now we we have to find A”, B” after rotation about point C (2,0) with a dilation factor of 2.
#A”(x, y) -> 2 * A’(x,y) - C (x,y)#
#A”((x),(y)) = 2 * ((-11), (-12)) - ((2), (0)) = ((-24),(-24))#
Similarly, #B”((x),(y)) = 2 * ((-10), (-12)) - ((2), (0)) = ((-22),(-24))#
New endpoints are #A”(-24, -24), B”(-22, -24)#
Distance of new points from origin
#vec(OA”) = sqrt(-24^2 + -24^2) = 33.94#
#vec(OB”) = sqrt(-22^2 + -24^2) = 32.56#]
#A (x,y) -> A’(x, y) = (5,2) -> ((2x’ - 5), (2y’ - 2) => (-11, -12)#
#A’(x,y) => ((-6 - 5), (-10 - 2) => (-11, -12)#
#B (x,y) - > B’ (x,y) = (4 , 2) -> ((2x’ - 4), (2y’ - 2) #
#B’(x,y) => ((-6 - 4), (-10 - 2) => (-10, -12)#
New coordinates after reflection are #A’(-11, -12), B’(-10, -12)#
Now we we have to find A”, B” after rotation about point C (2,0) with a dilation factor of 2.
#A”(x, y) -> 2 * A’(x,y) - C (x,y)#
#A”((x),(y)) = 2 * ((-11), (-12)) - ((2), (0)) = ((-24),(-24))#
Similarly, #B”((x),(y)) = 2 * ((-10), (-12)) - ((2), (0)) = ((-22),(-24))#
New endpoints are #A”(-24, -24), B”(-22, -24)#
Distance of new points from origin
#vec(OA”) = sqrt(-24^2 + -24^2) = 33.94#
#vec(OB”) = sqrt(-22^2 + -24^2) = 32.56#