Question

• reflections (flips, like with a mirror)
• rotations (spins or turns)

let’s review to get “warmed - up”.

1. translate △qrs if q(4,1), r(7, - 2), s(2,3) by moving it left 3 and down 4.
2. rotate △car if c(-1,-4), a(2,6), r(-4,-2) 180° around the origin.
3. what would be the new coordinates of △qrs in
4. what would be the coordinates of △car in prob

Explanation:

Step1: Translate coordinates of ΔQRS

For a translation left 3 and down 4, we subtract 3 from the x - coordinates and 4 from the y - coordinates.
For point Q(4,1): New x = 4 - 3=1, new y = 1 - 4=-3, so Q'=(1, - 3).
For point R(7,-2): New x = 7 - 3 = 4, new y=-2 - 4=-6, so R'=(4, - 6).
For point S(2,3): New x = 2 - 3=-1, new y = 3 - 4=-1, so S'=(-1, - 1).

Step2: Rotate coordinates of ΔCAR 180° around the origin

The rule for a 180° rotation around the origin is (x,y)→(-x,-y).
For point C(-1,-4): New x=-(-1) = 1, new y=-(-4)=4, so C'=(1,4).
For point A(2,6): New x=-2, new y=-6, so A'=(-2,-6).
For point R(-4,-2): New x=-(-4) = 4, new y=-(-2)=2, so R'=(4,2).

Answer:

1. Q'(1, - 3), R'(4, - 6), S'(-1, - 1)
2. C'(1,4), A'(-2,-6), R'(4,2)