Question

select from the drop - down menus to correctly complete the sentence
the rule $(x,y)\to(x + 2,y - 4)$ represents a translation 2 units choose and 4 units choose

Explanation:

Step1: Analyze the \(x\) - coordinate change

For a point \((x,y)\), the new \(x\) - coordinate is \(x + 2\). In the coordinate plane, when the \(x\) - coordinate of a point increases (\(x\to x + h\), \(h>0\)), the point moves to the right. Here \(h = 2\), so it moves 2 units to the right.

Step2: Analyze the \(y\) - coordinate change

The new \(y\) - coordinate is \(y-4\). In the coordinate plane, when the \(y\) - coordinate of a point decreases (\(y\to y - k\), \(k > 0\)), the point moves down. Here \(k = 4\), so it moves 4 units down.

Answer:

First blank: right; Second blank: down