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AP EAMCET · Maths · Three Dimensional Geometry

A plane meets the \(X, Y, Z\)-axes in \(A, B, C\) respectively. If the centroid of the \(\triangle A B C\) is \((2,-3,5)\), then the perpendicular distance from origin to the given plane is

  1. A \(\frac{7}{\sqrt{40}}\)
  2. B \(\frac{6}{7}\)
  3. C \(\frac{8}{\sqrt{50}}\)
  4. D \(\frac{90}{19}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{90}{19}\)

Step-by-step Solution

Detailed explanation

\[ \begin{aligned} & A=(a, 0,0), B \equiv(0, b, 0), C \equiv(0,0, c) \\ & \because \text { Centroid of } \triangle A B C \equiv\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right) \equiv(2,-3,5) \\ & \therefore a=6, b=-9, c=15 \end{aligned} \] Plane is…