Question

write the coordinates of the vertices after a dilation with a scale factor of \\( \frac { 1 } { 2 } \\) centered at the origin.
\\( r ^ { prime } ( \square, \square ) \\)
\\( s ^ { prime } ( \square, \square ) \\)
\\( t ^ { prime } ( \square, \square ) \\)
\\( u ^ { prime } ( \square, \square ) \\)

Explanation:

Step1: Find original coordinates

From the graph, \(R(-4,-6)\), \(S(8,-6)\), \(T(8,-2)\), \(U(-4,-2)\)

Step2: Apply dilation formula

The formula for dilation centered at the origin with scale factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = \frac{1}{2}\)

• For \(R(-4,-6)\): \(R'(\frac{1}{2}\times(-4),\frac{1}{2}\times(-6))=(-2,-3)\)
• For \(S(8,-6)\): \(S'(\frac{1}{2}\times8,\frac{1}{2}\times(-6))=(4,-3)\)
• For \(T(8,-2)\): \(T'(\frac{1}{2}\times8,\frac{1}{2}\times(-2))=(4,-1)\)
• For \(U(-4,-2)\): \(U'(\frac{1}{2}\times(-4),\frac{1}{2}\times(-2))=(-2,-1)\)

Answer:

\(R'(-2,-3)\)
\(S'(4,-3)\)
\(T'(4,-1)\)
\(U'(-2,-1)\)