Question

1. square defg with vertices ( d(0,0) ), ( e(2,4) ), ( f(6,2) ), and ( g(4,-2) ); ( k = 5/2 )

Explanation:

Step1: Apply dilation formula

For a dilation with scale factor \(k\) centered at the origin, the formula is \((x,y)\to(kx,ky)\).

Step2: Calculate \(D'\)

Given \(D(0,0)\) and \(k = \frac{5}{2}\), then \(D'=(0\times\frac{5}{2},0\times\frac{5}{2})=(0,0)\)

Step3: Calculate \(E'\)

Given \(E(2,4)\) and \(k=\frac{5}{2}\), then \(E'=(2\times\frac{5}{2},4\times\frac{5}{2})=(5,10)\)

Step4: Calculate \(F'\)

Given \(F(6,2)\) and \(k = \frac{5}{2}\), then \(F'=(6\times\frac{5}{2},2\times\frac{5}{2})=(15,5)\)

Step5: Calculate \(G'\)

Given \(G(4,- 2)\) and \(k=\frac{5}{2}\), then \(G'=(4\times\frac{5}{2},-2\times\frac{5}{2})=(10,-5)\)

Answer:

\(D'=(0,0)\), \(E'=(5,10)\), \(F'=(15,5)\), \(G'=(10,-5)\)