Question

which translation maps (\triangle rst) onto its image? 10 units down 10 units up 10 units to the right 10 units to the left

Explanation:

Step1: Analyze the change in x - coordinates

For point \(R(15,15)\) and \(R'(5,15)\), the x - coordinate changes from \(15\) to \(5\). The change in the x - coordinate is \(5 - 15=- 10\).
For point \(S(15, - 10)\) and \(S'(5,-10)\), the x - coordinate changes from \(15\) to \(5\). The change in the x - coordinate is \(5 - 15=-10\).
For point \(T(20,10)\) and \(T'(10,10)\), the x - coordinate changes from \(20\) to \(10\). The change in the x - coordinate is \(10 - 20=-10\).

Step2: Analyze the change in y - coordinates

For point \(R(15,15)\) and \(R'(5,15)\), the y - coordinate remains \(15\) (\(15 - 15 = 0\)).
For point \(S(15, - 10)\) and \(S'(5,-10)\), the y - coordinate remains \(-10\) (\(-10+10 = 0\)).
For point \(T(20,10)\) and \(T'(10,10)\), the y - coordinate remains \(10\) (\(10 - 10=0\)).

A translation of the form \((x,y)\to(x + a,y + b)\). Here \(a=-10\) (since \(x\) values decrease by \(10\)) and \(b = 0\). A negative change in the \(x\) - direction means a shift to the left.

Answer:

10 units to the left