What set of transformations could be applied to rectangle abcd to create a'b'c'd'? rectangle formed by ordered pairs a at negative 4, 2, b at negative 4, 1, c at negative 1, 1, d at negative 1, 2. second rectangle transformed formed by ordered pairs a prime at 2, negative 4, b prime 1, negative 4, c prime at 1, negative 1, d prime at 2, negative 1.

A set of transformations could be applied to rectangle ABCD to create A'B'C'D' is:

1) A rotation of 90° counterclockwise about the origin.

2) A reflection about the y-axis.

Solution:

1) We can rotate the rectangle ABCD an angle of 90° counterclockwise about the origin to obtain the rectangle EFGH.

When we rotate 90° counterclockwise with respect the origin, a point P=(x,y) changes to a point P'=(-y,x), then:

A=(-4, 2)=(xa, ya); xa=-4, ya=2→E=(-ya, xa)→E=(-2, -4)

B=(-4, 1)=(xb, yb); xb=-4, yb=1→F=(-yb, xb)→F=(-1, -4)

C=(-1, 1)=(xc, yc); xc=-1, yc=1→G=(-yc, xc)→G=(-1, -1)

D=(-1, 2)=(xd, yd); xd=-1, yd=2→D=(-yd, xd)→H=(-2, -1)

2) We make a reflection about the y-axis.

When we makes a reflection about the y-axis, a point P=(x,y) changes to a point

P'=(-x,y), then:

E=(-2, -4)=(xe, ye); xe=-2, ye=-4→A'=(-xe, ye)=(-(-2), -4)→A'=(2, -4)

F=(-1, -4)=(xf, yf); xf=-1, yf=-4→B'=(-xf, yf)=(-(-1), -4)→B'=(1, -4)

G=(-1, -1)=(xg, yg); xg=-1, yg=-1→C'=(-xg, yg)=(-(-1), -1)→C'=(1, -1)

H=(-2, -1)=(xh, yh); xh=-2, yh=-1→D'=(-xh, yh)=(-(-2), -1)→D'=(2, -1)

13cm

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