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 a point \((x,y)\) translated to \((x - 2,y+7)\), in the \(x\) - direction, if the transformation is \(x\to x - h\), when \(h>0\), the graph moves \(h\) units to the left. Here \(h = 2\), so the movement in the \(x\) - direction is \(2\) units to the left.

Step2: Analyze the y - coordinate change

In the \(y\) - direction, if the transformation is \(y\to y + k\), when \(k>0\), the graph moves \(k\) units up. Here \(k = 7\), so the movement in the \(y\) - direction is \(7\) units up.

Answer:

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