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Question

In parallelogram PQRS, P(-3,2), Q(2,7) and S(1,9) are three vertices. Then the length of diagonal PR is


  1. 25 units
  2. 15 units
  3. 12 units
  4. 9 units


Solution

The correct option is B 15 units

Draw PE, SF parallel to x-axis.

Draw QE, RF parallel to y-axis.

Now, in right triangles PEQ and SFR

PQ = SR

QPE = RSF

PQE = SRF

Therefore, PE = SF and QE = RF .....[by RHS congruency]

Hence, PE = SF = 2 - (-3) = 5 and QE = RF = 7 - 2 = 5

Now, x-coordinate of R = 1 + SF
                                       = 1 + 5
                                       = 6 

         y-coordinate of R = 9 + RF
                                       = 9 + 5
                                       = 14

Therefore coordinates of R(6,14).  

The distance between two points (x1,y1) and (x2,y2) is  (x2x1)2+(y2y1)2 

PR = (6(3)2+(142)2
         = 92+122
         = 225
         = 15 units

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