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 R's coordinates

Original \( R(15,15) \), image \( R'(5,15) \). The x - coordinate changes from 15 to 5, \( 15 - 5=10 \), y - coordinate stays 15.

Step2: Analyze S's coordinates

Original \( S(15, - 10) \), image \( S'(5, - 10) \). x - coordinate: \( 15 - 5 = 10 \), y - coordinate remains - 10.

Step3: Analyze T's coordinates

Original \( T(20,10) \), image \( T'(10,10) \). x - coordinate: \( 20 - 10=10 \), y - coordinate stays 10.
In a translation, when the x - coordinate decreases by 10 (and y - coordinate is constant), the figure moves 10 units to the left.

Answer:

D. 10 units to the left