Respuesta :

mhanifa

Given

  • R, S, Q and P are midpoints of OC, CB, BA and OA,
  • OR = a, CS = b and OP = c

To prove

  • RS is parallel to PQ

Solution

Find RS

  • RS = RC + CS = a + b, since RC = OR = a

Find AQ

  • AB = AO + OC + CB
  • AB = - 2c + 2a + 2b. since AO = -2OP = - 2c, OC = 2OR = 2a, CB = 2CS = 2c
  • AQ = 1/2AB = 1/2(- 2c + 2a + 2b) = - c + a + b

Find PQ

  • PQ = PA + AQ = c - c + a + b = a + b, since PA = OP = c

Compare RS and PQ

  • RS  =  PQ = a + b
  • Both vectors have same value, hence they are parallel.

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