Question

a square on a coordinate plane is translated 9 units down and 1 unit to the right. which function rule describes the translation?
t_{1,-9}(x,y)
t_{-1,-9}(x,y)
t_{-9,1}(x,y)
t_{-9,-1}(x,y)

Explanation:

Step1: Analyze horizontal translation

When a point \((x,y)\) is translated \(a\) units to the right, the \(x -\)coordinate changes as \(x\to x + a\). Here, \(a = 1\) (translation 1 unit to the right).

Step2: Analyze vertical translation

When a point \((x,y)\) is translated \(b\) units down, the \(y -\)coordinate changes as \(y\to y - b\). Here, \(b=9\) (translation 9 units down).
In the translation notation \(T_{h,k}(x,y)\), where \(h\) is the horizontal change and \(k\) is the vertical change. So \(h = 1\) and \(k=-9\)

Answer:

\(T_{1,-9}(x,y)\)