Question

the table shows the coordinates of the vertices of △rst and its image. △rst △rst r(15,15) r(5,15) s(15, - 10) s(5, - 10) t(20,10) t(10,10) 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

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

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 \(10\).

Since the y - coordinates of the vertices of \(\triangle RST\) and \(\triangle R'S'T'\) are the same, there is no vertical translation. The x - coordinates of the vertices of \(\triangle RST\) are decreased by \(10\) (i.e., \(x'=x - 10\)) to get the x - coordinates of the vertices of \(\triangle R'S'T'\). A decrease in the x - coordinate means a translation to the left.

Answer:

10 units to the left