Question

write the coordinates of the vertices after a dilation with a scale factor of 5, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of the vertices are \(D(-2,-2)\), \(E(-2,0)\), \(F(2,1)\), \(G(2, - 2)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 5\), the formula to find the new coordinates \((x',y')\) of a point \((x,y)\) is \((x',y')=(k\times x,k\times y)\)
For point \(D(-2,-2)\): \(x'=5\times(-2)=-10\), \(y'=5\times(-2)=-10\), new coordinates are \(D'(-10,-10)\)
For point \(E(-2,0)\): \(x'=5\times(-2)=-10\), \(y'=5\times0 = 0\), new coordinates are \(E'(-10,0)\)
For point \(F(2,1)\): \(x'=5\times2 = 10\), \(y'=5\times1=5\), new coordinates are \(F'(10,5)\)
For point \(G(2,-2)\): \(x'=5\times2 = 10\), \(y'=5\times(-2)=-10\), new coordinates are \(G'(10,-10)\)

Answer:

The new coordinates of the vertices are \(D'(-10,-10)\), \(E'(-10,0)\), \(F'(10,5)\), \(G'(10,-10)\)