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 - coordinate change

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

Step2: Analyze the y - coordinate change

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 x - coordinate of each vertex is decreased by \(10\) (i.e., \(x\to x - 10\)) and the y - coordinate remains the same (\(y\to y\)), the translation is \(10\) units to the left.

Answer:

10 units to the left