Question

write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.

Explanation:

Step1: Recall the rotation rule

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

Step2: Find the coordinates of each vertex

• For point \(D(0,-8)\):

Using the rule \((x = 0,y=-8)\to(y=-8,-x = 0)\), so \(D'\) is \((-8,0)\).

• For point \(E(0,0)\):

Using the rule \((x = 0,y = 0)\to(y = 0,-x=0)\), so \(E'\) is \((0,0)\).

• For point \(F(4,0)\):

Using the rule \((x = 4,y = 0)\to(y = 0,-x=-4)\), so \(F'\) is \((0,-4)\).

• For point \(G(4,-8)\):

Using the rule \((x = 4,y=-8)\to(y=-8,-x=-4)\), so \(G'\) is \((-8,-4)\).

Answer:

\(D'(-8,0)\), \(E'(0,0)\), \(F'(0,-4)\), \(G'(-8,-4)\)