Two arrows meeting at a right angle is exactly the same as their dot product being zero, a·b=0, which in coordinates reads x₁x₂+y₁y₂=0.
Module goal. Introduce the operation that multiplies two vectors into a number, capturing the angle between them, projection, and when they're perpendicular.
eastmath.com · 27.4 The Dot Product: Angles and Perpendicularity · 27.4.6 Testing for Perpendicularity