Question

the rule as a mapping for the translation of a rectangle is $(x,y)\to(x - 2,y + 7)$. 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 the x - coordinate change

For the x - coordinate, the rule is \(x
ightarrow x - 2\). In a coordinate plane, if \(x\) changes to \(x - h\) (\(h>0\)), the graph moves \(h\) units to the left. Here \(h = 2\), so the rectangle moves 2 units to the left.

Step2: Analyze the y - coordinate change

For the y - coordinate, the rule is \(y
ightarrow y+7\). In a coordinate plane, if \(y\) changes to \(y + k\) (\(k>0\)), the graph moves \(k\) units up. Here \(k = 7\), so the rectangle moves 7 units up.

Answer:

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