Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{4}$, centered at the origin.
$e(\square,\square)$
$f(\square,\square)$
$g(\square,\square)$
$h(\square,\square)$

Explanation:

Step1: Find original coordinates

From the graph, \(E(- 8,-8)\), \(F(8,-8)\), \(G(4,8)\), \(H(0,8)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \(k = \frac{1}{4}\), the formula is \((x,y)\to(kx,ky)\).

• For \(E(-8,-8)\): \(E'(\frac{1}{4}\times(-8),\frac{1}{4}\times(-8))=(-2,-2)\)
• For \(F(8,-8)\): \(F'(\frac{1}{4}\times8,\frac{1}{4}\times(-8))=(2,-2)\)
• For \(G(4,8)\): \(G'(\frac{1}{4}\times4,\frac{1}{4}\times8)=(1,2)\)
• For \(H(0,8)\): \(H'(\frac{1}{4}\times0,\frac{1}{4}\times8)=(0,2)\)

Answer:

\(E'(-2,-2)\), \(F'(2,-2)\), \(G'(1,2)\), \(H'(0,2)\)