Question

write the coordinates of the vertices after a rotation 90° counterclockwise around origin.
q ( , )
r ( , )
s ( , )
t ( , )

Explanation:

Step1: Recall the rotation rule

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

Step2: Find the coordinates of \(Q\)

The original coordinates of \(Q\) are \((- 4,-9)\). Using the rotation rule \((x = - 4,y=-9)\), we get \(x'=-y = 9\) and \(y'=x=-4\). So \(Q'=(9,-4)\).

Step3: Find the coordinates of \(R\)

The original coordinates of \(R\) are \((-4,-3)\). Using the rotation rule \((x=-4,y = - 3)\), we get \(x'=-y = 3\) and \(y'=x=-4\). So \(R'=(3,-4)\).

Step4: Find the coordinates of \(S\)

The original coordinates of \(S\) are \((0,-3)\). Using the rotation rule \((x = 0,y=-3)\), we get \(x'=-y = 3\) and \(y'=x = 0\). So \(S'=(3,0)\).

Step5: Find the coordinates of \(T\)

The original coordinates of \(T\) are \((0,-9)\). Using the rotation rule \((x = 0,y=-9)\), we get \(x'=-y = 9\) and \(y'=x = 0\). So \(T'=(9,0)\).

Answer:

\(Q'(9,-4)\), \(R'(3,-4)\), \(S'(3,0)\), \(T'(9,0)\)