Final answer:
The vertices of triangle KLM are transformed first by sliding left two units to obtain K(1,3), L(3,4), and M(-2,6), and subsequently sliding down five units to get K(1,-2), L(3,-1), and M(-2,1).
Step-by-step explanation:
The correct answer is that after sliding the triangle to the left by two units, the new vertices will be K(1,3), L(3,4), and M(-2,6). When we slide the triangle down by five units, the new vertices will become K(1,-2), L(3,-1), and M(-2,1).
- To move the triangle left by two units, we subtract 2 from the x-coordinate of each vertex.
- K(3,3) becomes K(3-2,3) which is K(1,3).
- L(5,4) becomes L(5-2,4) which is L(3,4).
- M(0,6) becomes M(0-2,6) which is M(-2,6).
- To move the triangle down by five units, we subtract 5 from the y-coordinate of each vertex.
- K(1,3) becomes K(1,3-5) which is K(1,-2).
- L(3,4) becomes L(3,4-5) which is L(3,-1).
- M(-2,6) becomes M(-2,6-5) which is M(-2,1).
These operations on the coordinates follow the principles of vector subtraction, which is akin to the physical displacement described in the given scenarios. The transformations are a simple translation of the triangle along one axis at a time.