Question

180⁰ rotation
rule (x, y): (□, □)
t (□, □)
u (□, □)
v (□, □)
w (□, □)

Explanation:

Step1: Recall 180° rotation rule

The rule for a \(180^\circ\) rotation about the origin is \((x,y)\to(-x,-y)\).

Step2: Find coordinates of original points

From the graph:

• \(T\): Let's identify \(T\)'s coordinates. Looking at the grid, \(T\) is at \((1, - 4)\).
• \(U\): \(U\) is at \((4, - 4)\).
• \(V\): \(V\) is at \((4, - 1)\).
• \(W\): \(W\) is at \((1, - 1)\).

Step3: Apply 180° rotation rule to each point

• For \(T(1,-4)\): Apply \((x,y)\to(-x,-y)\), so \(T'\) (rotated \(T\)) is \((-1,4)\).
• For \(U(4,-4)\): Apply the rule, \(U'\) is \((-4,4)\).
• For \(V(4,-1)\): Apply the rule, \(V'\) is \((-4,1)\).
• For \(W(1,-1)\): Apply the rule, \(W'\) is \((-1,1)\).

Answer:

Rule \((x,y)\to\boldsymbol{(-x,-y)}\)

\(T\): \(\boldsymbol{(-1,4)}\)

\(U\): \(\boldsymbol{(-4,4)}\)

\(V\): \(\boldsymbol{(-4,1)}\)

\(W\): \(\boldsymbol{(-1,1)}\)