Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of the vertices are \(T(-4, - 4)\), \(U(-4,-2)\), \(V(-2,-2)\), \(W(-2,-4)\).

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 \(x'=k\times x\) and \(y'=k\times y\).
For point \(T\): \(x_T'=2\times(-4)=-8\), \(y_T'=2\times(-4)=-8\)
For point \(U\): \(x_U'=2\times(-4)=-8\), \(y_U'=2\times(-2)=-4\)
For point \(V\): \(x_V'=2\times(-2)=-4\), \(y_V'=2\times(-2)=-4\)
For point \(W\): \(x_W'=2\times(-2)=-4\), \(y_W'=2\times(-4)=-8\)

Answer:

\(T'(-8,-8)\)
\(U'(-8,-4)\)
\(V'(-4,-4)\)
\(W'(-4,-8)\)