Question

which type of transformation is described by (x, y) → (x + 2, y + 3)?
a a translation 2 units to the right and 3 units down
b a translation 2 units to the left and 3 units down
c a translation 2 units to the right and 3 units up
d a translation 2 units to the left and 3 units up

Explanation:

Step1: Analyze x - coordinate change

In the transformation $(x,y)\to(x + 2,y+3)$, for the x - coordinate, we have $x\to x + 2$. Adding a positive number to the x - coordinate moves the point to the right. Since we add 2 to x, the point moves 2 units to the right.

Step2: Analyze y - coordinate change

For the y - coordinate, we have $y\to y + 3$. Adding a positive number to the y - coordinate moves the point up. Since we add 3 to y, the point moves 3 units up.

Answer:

C. a translation 2 units to the right and 3 units up