1. What is the distance between the z – intercept from the x – intercept in the equation ax + by + cz + d = 0

• d sqrt(1/a^2 + 1/c^2)
  Expln:
  ax + by + cz + d = 0
  At the z-intercept, 'x' and 'y' are both zero.
  cz + d = 0 --> z = -d/c --> The z-intercept is the point (0, 0, -d/c).
  At the x-intercept, 'y' and 'z' are zero.
  ax + d = 0 --> x = -d/a --> The x-intercept is the point (-d/a, 0, 0).
  The distance between the points (0, 0, -d/c) and (-d/a, 0, 0) is
  
  sqrt[(-d/a)^2 + (-d/c)^2]
  = sqrt (d^2/a^2 + d^2/c^2)
  = d sqrt(1/a^2 + 1/c^2)
• 12 years agoHelpfull: Yes(3) No(1)