how can ı solve this example

[proper halo]

how can ı solve this example

[high nimbus]

One course of action is to graph. You can graph the line. Then, find a line that is perpendicular and also intersects (3,2). Use this perpendicular line to find the symmetric partner.

The more vector-themed way of solving is to use vector projection. We’re gonna construct a right triangle, cuz mathematicians loveeee triangles. Pick any arbitrary point A on that line (but preferably pick one with easy numbers to do math with). Find the vector V from that point A to (3,2). And you also have the vector U parallel to your line, <4, -1>. Project V onto U, and you’ll have one component of your right triangle. Use vector subtraction to find the third side. That is the distance vector from point (3,2) to the line. Flip it and add it to (3,2) twice to get it over the other side of the line to its symmetric partner