Question

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the table shows the coordinates of the vertices of △rst and its image. which translation maps △rst onto its image? 10 units down 10 units up 10 units to the right 10 units to the left

Explanation:

Step1: Analyze the x - coordinates of the vertices

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 y - coordinates of the vertices

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

A translation of the form \((x,y)\to(x + a,y + b)\). Since \(y\) - coordinates are unchanged (\(b = 0\)) and \(x\) - coordinates decrease by \(10\) (\(a=-10\)), the translation is \(10\) units to the left.

Answer:

10 units to the left