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AP EAMCET · Maths · Three Dimensional Geometry

In a triangle ABC, if the mid points of sides AB,BC,CA are (3,0,0),(0,4,0),(0,0,5), respectively, then AB2+BC2+CA2=

  1. A 50
  2. B 200
  3. C 300
  4. D 400
Verified Solution

Answer & Solution

Correct Answer

(D) 400

Step-by-step Solution

Detailed explanation

The midpoints of the sides are given as, AB,BC and CA are 3,0,0,0,4,0,0,0,5 The coordinates of A,B and C A=3,-4,5 B=3,4,-5 C=-3,4,5 And AB2=x2-x12+y2-y12+z2-z12 =(3-3)2+(4+4)2+(-5-5)2 =82+102 =164 Similarly, BC2=(-3-3)2+(4-4)2+(5+5)2 =36+100 =136 Similarly,…