Question

write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.
d((□, □))
e((□, □))
f((□, □))
g((□, □))

Explanation:

Step1: Recall the rotation rule

When rotating a point \((x,y)\) \(270^{\circ}\) counter - clockwise around the origin, the new coordinates \((x',y')\) follow the rule \((x,y)\to(y, - x)\).

Step2: Find the coordinates of \(D\)

The coordinates of \(D\) are \((4,7)\). Using the rule \((x,y)\to(y, - x)\), for \(x = 4\) and \(y = 7\), we get \(D'(7,-4)\).

Step3: Find the coordinates of \(E\)

The coordinates of \(E\) are \((4,10)\). Using the rule \((x,y)\to(y, - x)\), for \(x = 4\) and \(y = 10\), we get \(E'(10,-4)\).

Step4: Find the coordinates of \(F\)

The coordinates of \(F\) are \((6,10)\). Using the rule \((x,y)\to(y, - x)\), for \(x = 6\) and \(y = 10\), we get \(F'(10,-6)\).

Step5: Find the coordinates of \(G\)

The coordinates of \(G\) are \((6,7)\). Using the rule \((x,y)\to(y, - x)\), for \(x = 6\) and \(y = 7\), we get \(G'(7,-6)\).

Answer:

\(D'(7,-4)\), \(E'(10,-4)\), \(F'(10,-6)\), \(G'(7,-6)\)