Question

1. triangle lmn is plotted on a coordinate plane. it is translated 5 units left and 3 units up. how is this sequence of transformations written in coordinate notation to correctly map triangle lmn to its image, triangle lmn? (x,y)→(x+3, y-5) (x,y)→(x-5, y+3) (x,y)→(x+5,y+3) (x,y)→(x+3,y+5)

Explanation:

Step1: Recall translation rules

In coordinate plane, translating a point \((x,y)\) \(a\) units left means subtracting \(a\) from the \(x\)-coordinate, and translating \(b\) units up means adding \(b\) to the \(y\)-coordinate.

Step2: Apply the rules

Here, the translation is 5 units left (so \(x\)-coordinate: \(x - 5\)) and 3 units up (so \(y\)-coordinate: \(y+3\)). So the transformation is \((x,y)\to(x - 5,y + 3)\).

Answer:

\((x,y)\to(x - 5,y + 3)\) (the second option among the given choices)