Question

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 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 \(15\).
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 of \(\triangle RST\) 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