Question

4 which of the following dilations are reductions? select two correct answer choices. a (x, y)→(0.4x, 0.4y) b (x, y)→(3x, 3y) c (x,y)→(\frac{5}{2}x, \frac{5}{2}y) d (x, y)→(1.25x, 1.25y) e (x, y)→(\frac{8}{9}x, \frac{8}{9}y)

Explanation:

Step1: Recall dilation rule

A dilation is a reduction if the scale factor \(k\) is between \(0\) and \(1\). For a dilation \((x,y)\to(kx,ky)\), we check the value of \(k\).

Step2: Analyze option A

For \((x,y)\to(0.4x,0.4y)\), the scale - factor \(k = 0.4\). Since \(0<0.4<1\), it is a reduction.

Step3: Analyze option B

For \((x,y)\to(3x,3y)\), the scale - factor \(k = 3\). Since \(3>1\), it is an enlargement.

Step4: Analyze option C

For \((x,y)\to(\frac{5}{2}x,\frac{5}{2}y)\), and \(\frac{5}{2}=2.5>1\), it is an enlargement.

Step5: Analyze option D

For \((x,y)\to(1.25x,1.25y)\), since \(1.25 > 1\), it is an enlargement.

Step6: Analyze option E

For \((x,y)\to(\frac{8}{9}x,\frac{8}{9}y)\), and \(0<\frac{8}{9}<1\), it is a reduction.

Answer:

A. \((x,y)\to(0.4x,0.4y)\), E. \((x,y)\to(\frac{8}{9}x,\frac{8}{9}y)\)