Question

graph the image of rectangle cdef after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original vertices

The vertices of rectangle CDEF are C(-4,-5), D(5,-5), E(5,1), F(-4,1).

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 2\), the formula to find the new coordinates \((x',y')\) of a point \((x,y)\) is \((x',y')=(k\cdot x,k\cdot y)\).
For point C(-4,-5):
\(x'=2\times(-4)= - 8\), \(y'=2\times(-5)=-10\), so \(C'(-8,-10)\).
For point D(5,-5):
\(x'=2\times5 = 10\), \(y'=2\times(-5)=-10\), so \(D'(10,-10)\).
For point E(5,1):
\(x'=2\times5 = 10\), \(y'=2\times1 = 2\), so \(E'(10,2)\).
For point F(-4,1):
\(x'=2\times(-4)=-8\), \(y'=2\times1 = 2\), so \(F'(-8,2)\).

Step3: Graph new rectangle

Plot the points \(C'(-8,-10)\), \(D'(10,-10)\), \(E'(10,2)\), \(F'(-8,2)\) and connect them to form the dilated rectangle.

Answer:

The new vertices of the dilated rectangle are \(C'(-8,-10)\), \(D'(10,-10)\), \(E'(10,2)\), \(F'(-8,2)\). Graph by plotting these points and connecting them.