Question

a shape is translated by 5 units to the right and 5 units down. which of the following represents the transformation algebraically?
show your work here
\\(\circ\\) \\((x,y) \to (x - 4,y + 4)\\) \\(\quad\\) \\(\bullet\\) \\((x,y) \to (x + 5,y - 5)\\)
\\(\circ\\) \\((x,y) \to (x - 5,y + 5)\\) \\(\quad\\) \\(\circ\\) \\((x,y) \to (x - 6,y + 6)\\)

Explanation:

Step1: Recall translation rules

In coordinate geometry, a translation of \( h \) units right/left and \( k \) units up/down is given by \((x,y)\to(x + h,y + k)\), where \( h>0 \) is right, \( h<0 \) is left, \( k>0 \) is up, \( k<0 \) is down.

Step2: Apply the given translation

The shape is translated 5 units right (\( h = 5 \)) and 5 units down (\( k=- 5 \)). So the transformation is \((x,y)\to(x + 5,y-5)\).

Answer:

\((x,y)\to(x + 5,y - 5)\) (the option with this transformation)