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What is the distance between the z-intercept from the x intercept in the equation ax plus by plus cz plus d equals 0?
Wiki User
∙ 13y ago
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 (d2/a2 + d2/c2) = d sqrt(1/a2 + 1/c2)
Wiki User
∙ 13y ago
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