Question

which type of transformation is described by $(x,y)\to(x + 2,y + 3)$?
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:

In a coordinate transformation \((x,y)\to(x + a,y + b)\), if \(a>0\), the graph moves \(a\) units to the right (since \(x\) - coordinate increases), and if \(b>0\), the graph moves \(b\) units up (since \(y\) - coordinate increases). Here \(a = 2\) (positive) and \(b=3\) (positive).

Answer:

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