Question

write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.

Explanation:

Step1: Find original coordinates

The original coordinates are \(D(-4,1)\), \(E(0,1)\), \(F(0,10)\), \(G(-4,10)\)

Step2: Apply rotation rule

The rule for a \(90^{\circ}\) counter - clockwise rotation around the origin is \((x,y)\to(-y,x)\)
For point \(D(-4,1)\):
Substitute \(x = - 4\) and \(y = 1\) into the rule \((x,y)\to(-y,x)\)
\((-4,1)\to(-1,-4)\)
For point \(E(0,1)\):
Substitute \(x = 0\) and \(y = 1\) into the rule \((x,y)\to(-y,x)\)
\((0,1)\to(-1,0)\)
For point \(F(0,10)\):
Substitute \(x = 0\) and \(y = 10\) into the rule \((x,y)\to(-y,x)\)
\((0,10)\to(-10,0)\)
For point \(G(-4,10)\):
Substitute \(x=-4\) and \(y = 10\) into the rule \((x,y)\to(-y,x)\)
\((-4,10)\to(-10,-4)\)

Answer:

The new coordinates are \(D'(-1,-4)\), \(E'(-1,0)\), \(F'(-10,0)\), \(G'(-10,-4)\)