Question

the rule as a mapping for the translation of a rectangle is (x, y) → (x − 2, y + 7). which describes this translation?
○ a translation of 2 units down and 7 units to the right
○ a translation of 2 units down and 7 units to the left
○ a translation of 2 units to the right and 7 units up
○ a translation of 2 units to the left and 7 units up

Explanation:

Step1: Analyze x - coordinate change

In the translation rule \((x,y)\to(x - 2,y + 7)\), for the x - coordinate, we have \(x\) changing to \(x-2\). In the coordinate system, when the x - coordinate of a point \((x,y)\) is transformed as \(x\to x - a\) (\(a>0\)), the point moves \(a\) units to the left. Here \(a = 2\), so the point moves 2 units to the left.

Step2: Analyze y - coordinate change

For the y - coordinate, we have \(y\) changing to \(y + 7\). In the coordinate system, when the y - coordinate of a point \((x,y)\) is transformed as \(y\to y + b\) (\(b>0\)), the point moves \(b\) units up. Here \(b=7\), so the point moves 7 units up.

Answer:

a translation of 2 units to the left and 7 units up