Question

1. trapezoid qrst with vertices q(2,1), r(2,5), s(4,5), and t(8,1): 90° clockwise q (_, _) r (_, _) s (_, _) t (_, _)

Explanation:

Step1: Recall the rule for \(90^{\circ}\) clockwise rotation

The rule for a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, - x)\)

Step2: Apply the rule to point \(Q(2,1)\)

For \(Q(2,1)\), \(x = 2\) and \(y=1\). Using the formula \((x,y)\to(y,-x)\), we get \(Q'(1,- 2)\)

Step3: Apply the rule to point \(R(2,5)\)

For \(R(2,5)\), \(x = 2\) and \(y = 5\). Using the formula \((x,y)\to(y,-x)\), we get \(R'(5,-2)\)

Step4: Apply the rule to point \(S(4,5)\)

For \(S(4,5)\), \(x = 4\) and \(y = 5\). Using the formula \((x,y)\to(y,-x)\), we get \(S'(5,-4)\)

Step5: Apply the rule to point \(T(8,1)\)

For \(T(8,1)\), \(x = 8\) and \(y = 1\). Using the formula \((x,y)\to(y,-x)\), we get \(T'(1,-8)\)

Answer:

\(Q'(1,-2)\), \(R'(5,-2)\), \(S'(5,-4)\), \(T'(1,-8)\)