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 mapping $(x,y)\to(x - 2,y + 7)$, for the x - coordinate, when we go from $x$ to $x-2$, the value of $x$ decreases by 2. In a coordinate - plane, a decrease in the x - value means a shift to the left.

Step2: Analyze y - coordinate change

For the y - coordinate, when we go from $y$ to $y + 7$, the value of $y$ increases by 7. In a coordinate - plane, an increase in the y - value means a shift upwards.

Answer:

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