The segment from (-1,4) to (2,-2) extended three times then terminal point of segment is

There are various ways in which you could do this problem.  I'm going to share what I think is one of the faster ways.

Instead of thinking of jumping from (-1,4) TO (2,-2),  Consider the horiz. jump separately and the vertical jump separately.  From -1 to 2 is 3 units.  Three times that is 9 units.  Add 9 to -1, obtaining 8.  That's the horiz. component of the terminal point.

From 4 to -2 is -6 units.  Mult. that by 3.  The result is the vert. comp of the terminal point. 

When two lines intersect, they form two pairs of equal angles, which, taking one of each, add up to 180°. (jargon: angles forming a straight line   show more