Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{2}$, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of the vertices are \(K(4,- 8)\), \(N(8,-8)\), \(L(4,4)\), \(M(8,4)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = \frac{1}{2}\), 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 \(K(4,-8)\):
\(x'_K=\frac{1}{2}\times4 = 2\), \(y'_K=\frac{1}{2}\times(-8)=-4\)
For point \(N(8,-8)\):
\(x'_N=\frac{1}{2}\times8 = 4\), \(y'_N=\frac{1}{2}\times(-8)=-4\)
For point \(L(4,4)\):
\(x'_L=\frac{1}{2}\times4 = 2\), \(y'_L=\frac{1}{2}\times4 = 2\)
For point \(M(8,4)\):
\(x'_M=\frac{1}{2}\times8 = 4\), \(y'_M=\frac{1}{2}\times4 = 2\)

Answer:

The new coordinates of the vertices are \(K'(2,-4)\), \(N'(4,-4)\), \(L'(2,2)\), \(M'(4,2)\)