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, we have $x\to x-2$. A subtraction of 2 from the x - coordinate means a shift of 2 units to the left since in the coordinate plane, decreasing the x - value moves a point leftward.

Step2: Analyze y - coordinate change

For the y - coordinate, we have $y\to y + 7$. An addition of 7 to the y - coordinate means a shift of 7 units up since increasing the y - value moves a point upward in the coordinate plane.

Answer:

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