Question

∆ABC is translated 2 units down and 1 unit to the left. Then it is rotated 90° clockwise about the origin to form ∆A′B′C′. Whats the new coordinates?

Answer 1

Answer: The new coordinates are:

A'=(-2, 1)

B'=(-1,0)

C'=(1,0)

Solution:

A=(0,0); B=(1,1); C=(1,3)

1) Translation 2 units down and 1 unit to the left

When we translate a point P=(x,y) 2 units down and 1 unit to the left, the new coordinates of the point are P'=(x-1, y-2), then:

A=(0, 0)=(xa, ya); xa=0, ya=0→D=(xa-1, ya-2)=(0-1, 0-2)→D=(-1, -2)

B=(1, 1)=(xb, yb); xb=1, yb=1→E=(xb-1, yb-2)=(1-1, 1-2)→E=(0, -1)

C=(1, 3)=(xc, yc); xc=1, yc=3→F=(xc-1, yc-2)=(1-1, 3-2)→F=(0, 1)

2) Rotation 90° clockwise about the origin

When we rotate a point P=(x,y) an angle of 90° clockwise about the origin the new coordinates of the point are P'=(y, -x), then:

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

E=(0, -1)=(xe, ye); xe=0, ye=-1→B'=(ye, -xe)=(-1, -0)→B'=(-1, 0)

F=(0, 1)=(xf, yf); xf=0, yf=1→C'=(yf, -xf)=(1, -0)→C'=(1, 0)