Part of CG-01 — Straight Lines

Foot of Perpendicular and Image

by Notetube Official76 words4 views

For point P(x1, y1) and line ax + by + c = 0:

  • Foot of perpendicular F(h, k): hx1a\frac{h - x1}{a} = ky1b\frac{k - y1}{b} = -ax1+by1+c(a2+b2)\frac{ax1 + by1 + c}{(a^2 + b^2)}
  • Image Q(h, k): hx1a\frac{h - x1}{a} = ky1b\frac{k - y1}{b} = -2ax1+by1+c(a2+b2)\frac{ax1 + by1 + c}{(a^2 + b^2)}

The image formula has a factor of -2 (foot has -1). The foot F is the midpoint of P and its image Q.

Like these notes? Save your own copy and start studying with NoteTube's AI tools.

Sign up free to clone these notes