Question

which of the following algebraic rules represents a dilation that is an enlargement? (0.1x, 0.1y) (\frac{1}{3}x, \frac{1}{3}y) (\frac{5}{2}x, \frac{5}{2}y) (\frac{5}{6}x, \frac{5}{6}y) clear my selection

Explanation:

Step1: Recall dilation rule

For a dilation \((kx, ky)\), if \(k> 1\), it is an enlargement.

Step2: Check each option

• For \((0.1x,0.1y)\), \(k = 0.1<1\), it is a reduction.
• For \((\frac{1}{3}x,\frac{1}{3}y)\), \(k=\frac{1}{3}\approx0.33<1\), it is a reduction.
• For \((\frac{5}{2}x,\frac{5}{2}y)\), \(k = \frac{5}{2}=2.5>1\), it is an enlargement.
• For \((\frac{5}{6}x,\frac{5}{6}y)\), \(k=\frac{5}{6}\approx0.83<1\), it is a reduction.

Answer:

\((\frac{5}{2}x,\frac{5}{2}y)\)