Question

write the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

Explanation:

Step1: Identify original coordinates

Let's assume the original coordinates of the vertices of the rectangle are \(E(-8, - 2)\), \(F(-2,-2)\), \(G(-2,-10)\), \(H(-8,-10)\). The rule for a \(180^{\circ}\) counter - clockwise rotation around the origin is \((x,y)\to(-x,-y)\).

Step2: Apply rotation rule to point E

For point \(E(-8,-2)\), when we apply the rule \((x,y)\to(-x,-y)\), we get \(E'(8,2)\).

Step3: Apply rotation rule to point F

For point \(F(-2,-2)\), using the rule \((x,y)\to(-x,-y)\), we get \(F'(2,2)\).

Step4: Apply rotation rule to point G

For point \(G(-2,-10)\), applying the rule \((x,y)\to(-x,-y)\), we get \(G'(2,10)\).

Step5: Apply rotation rule to point H

For point \(H(-8,-10)\), using the rule \((x,y)\to(-x,-y)\), we get \(H'(8,10)\).

Answer:

The new coordinates of the vertices are \(E'(8,2)\), \(F'(2,2)\), \(G'(2,10)\), \(H'(8,10)\)