Question

1. max wrote the rule (x,y)→(5x,5y) to represent the dilation below. is max’s rule correct? explain.

Explanation:

Step1: Recall dilation rule concept

In a dilation centered at the origin, if the scale - factor is \(k\), the rule for a point \((x,y)\) is \((x,y)\to(kx,ky)\).

Step2: Analyze Max's rule

Max's rule is \((x,y)\to(5x,5y)\), which means the scale - factor \(k = 5\). This rule multiplies the \(x\) and \(y\) coordinates of each point of the pre - image by 5. For a dilation centered at the origin, this is the correct way to represent a dilation with a scale - factor of 5.

Answer:

Max's rule is correct. A dilation centered at the origin with a scale - factor \(k = 5\) has the rule \((x,y)\to(5x,5y)\) which multiplies the \(x\) and \(y\) coordinates of each point of the pre - image by 5.