The rule ro, 90° • t-1, 1(x, y) is applied to δbcd to produce δb"c"d". point b" of the final image is at (–4, 1).

what are the coordinates of point b on the pre-image?

a) (–2, –5)
b) (0, –5)
c) (2, 3)
d) (5, 0)

The coordinates of point B on the pre-image is (2, 3) :

RO, 90°
Original coordinates: (2 , 3)
Angle of roration 90
x-new = x*cos( θ )-ysin( θ ) , θ = 90
= 2cos(90) - 3sin(90)
x-new = (2)(0)-(3)(1) = -3
y-new = x*sins( θ)+ycos( θ ) , θ = 90
= 2sin(90) + 3cos(90)
y-new = (2)(1)+(3)(0) = 2
Coordinates after rotation (-3,2)

T-1
(-3,-1,2-1)
(-4,1)

1(-4,1) = (-4,1)

The rule RO, 90° • T-1, 1(x, y) is applied to ΔBCD to produce ΔB"C"D" means that it starts with T-1, 1(x, y) and ends with RO, 90° (counter-clockwise).

Working backward, we have

 RO, -90° (clockwise) which gives

(-4,1) => (1,4)

then reverse T-1, 1(x, y), which is T1, -1(x, y):

(1,4) => (2,3)

so ans is C

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